id int64 1 14M | domain stringclasses 6
values | topic stringclasses 23
values | subtopic stringclasses 37
values | difficulty int64 1 8 | unit_type stringclasses 3
values | title stringlengths 14 86 | content stringlengths 203 553 | key_equations stringclasses 23
values | prerequisites stringclasses 29
values | learning_objective stringclasses 37
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2,201 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 30.69 m | An object of mass 18.47 kg is released from rest at height 30.69 m above a reference level. Taking gravitational potential energy as m g h and kinetic energy as (1/2) m v², conservation of mechanical energy (neglecting non-conservative work) yields (1/2) m v² = m g h, so v = sqrt(2 g h) = 24.54 m/s at the reference lev... | K + U = constant (conservative systems); U_g = m g h; K = (1/2) m v^2 | newton_second_law; work-energy theorem | Apply conservation of mechanical energy to free-fall motion. |
2,202 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 4.17 m | An object of mass 11.44 kg is released from rest at height 4.17 m above a reference level. Taking gravitational potential energy as m g h and kinetic energy as (1/2) m v², conservation of mechanical energy (neglecting non-conservative work) yields (1/2) m v² = m g h, so v = sqrt(2 g h) = 9.044 m/s at the reference leve... | K + U = constant (conservative systems); U_g = m g h; K = (1/2) m v^2 | newton_second_law; work-energy theorem | Apply conservation of mechanical energy to free-fall motion. |
2,203 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 28.09 m | An object of mass 16.09 kg is released from rest at height 28.09 m above a reference level. Taking gravitational potential energy as m g h and kinetic energy as (1/2) m v², conservation of mechanical energy (neglecting non-conservative work) yields (1/2) m v² = m g h, so v = sqrt(2 g h) = 23.47 m/s at the reference lev... | K + U = constant (conservative systems); U_g = m g h; K = (1/2) m v^2 | newton_second_law; work-energy theorem | Apply conservation of mechanical energy to free-fall motion. |
2,204 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 12.76 m | An object of mass 2.126 kg is released from rest at height 12.76 m above a reference level. Taking gravitational potential energy as m g h and kinetic energy as (1/2) m v², conservation of mechanical energy (neglecting non-conservative work) yields (1/2) m v² = m g h, so v = sqrt(2 g h) = 15.82 m/s at the reference lev... | K + U = constant (conservative systems); U_g = m g h; K = (1/2) m v^2 | newton_second_law; work-energy theorem | Apply conservation of mechanical energy to free-fall motion. |
2,205 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 30.78 m | An object of mass 12.96 kg is released from rest at height 30.78 m above a reference level. Taking gravitational potential energy as m g h and kinetic energy as (1/2) m v², conservation of mechanical energy (neglecting non-conservative work) yields (1/2) m v² = m g h, so v = sqrt(2 g h) = 24.57 m/s at the reference lev... | K + U = constant (conservative systems); U_g = m g h; K = (1/2) m v^2 | newton_second_law; work-energy theorem | Apply conservation of mechanical energy to free-fall motion. |
2,206 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 37.92 m | An object of mass 9.517 kg is released from rest at height 37.92 m above a reference level. Taking gravitational potential energy as m g h and kinetic energy as (1/2) m v², conservation of mechanical energy (neglecting non-conservative work) yields (1/2) m v² = m g h, so v = sqrt(2 g h) = 27.27 m/s at the reference lev... | K + U = constant (conservative systems); U_g = m g h; K = (1/2) m v^2 | newton_second_law; work-energy theorem | Apply conservation of mechanical energy to free-fall motion. |
2,207 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 35.88 m | An object of mass 3.046 kg is released from rest at height 35.88 m above a reference level. Taking gravitational potential energy as m g h and kinetic energy as (1/2) m v², conservation of mechanical energy (neglecting non-conservative work) yields (1/2) m v² = m g h, so v = sqrt(2 g h) = 26.53 m/s at the reference lev... | K + U = constant (conservative systems); U_g = m g h; K = (1/2) m v^2 | newton_second_law; work-energy theorem | Apply conservation of mechanical energy to free-fall motion. |
2,208 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 14.86 m | An object of mass 5.309 kg is released from rest at height 14.86 m above a reference level. Taking gravitational potential energy as m g h and kinetic energy as (1/2) m v², conservation of mechanical energy (neglecting non-conservative work) yields (1/2) m v² = m g h, so v = sqrt(2 g h) = 17.07 m/s at the reference lev... | K + U = constant (conservative systems); U_g = m g h; K = (1/2) m v^2 | newton_second_law; work-energy theorem | Apply conservation of mechanical energy to free-fall motion. |
2,209 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 36.73 m | An object of mass 3.83 kg is released from rest at height 36.73 m above a reference level. Taking gravitational potential energy as m g h and kinetic energy as (1/2) m v², conservation of mechanical energy (neglecting non-conservative work) yields (1/2) m v² = m g h, so v = sqrt(2 g h) = 26.84 m/s at the reference leve... | K + U = constant (conservative systems); U_g = m g h; K = (1/2) m v^2 | newton_second_law; work-energy theorem | Apply conservation of mechanical energy to free-fall motion. |
2,210 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 34.5 m | An object of mass 6.74 kg is released from rest at height 34.5 m above a reference level. Taking gravitational potential energy as m g h and kinetic energy as (1/2) m v², conservation of mechanical energy (neglecting non-conservative work) yields (1/2) m v² = m g h, so v = sqrt(2 g h) = 26.01 m/s at the reference level... | K + U = constant (conservative systems); U_g = m g h; K = (1/2) m v^2 | newton_second_law; work-energy theorem | Apply conservation of mechanical energy to free-fall motion. |
2,211 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 19.76 m | An object of mass 6.63 kg is released from rest at height 19.76 m above a reference level. Taking gravitational potential energy as m g h and kinetic energy as (1/2) m v², conservation of mechanical energy (neglecting non-conservative work) yields (1/2) m v² = m g h, so v = sqrt(2 g h) = 19.68 m/s at the reference leve... | K + U = constant (conservative systems); U_g = m g h; K = (1/2) m v^2 | newton_second_law; work-energy theorem | Apply conservation of mechanical energy to free-fall motion. |
2,212 | physics | mechanics | mechanical_energy | 4 | worked_example | Conservation of mechanical energy: drop from height 4.959 m | An object of mass 1.494 kg is released from rest at height 4.959 m above a reference level. Taking gravitational potential energy as m g h and kinetic energy as (1/2) m v², conservation of mechanical energy (neglecting non-conservative work) yields (1/2) m v² = m g h, so v = sqrt(2 g h) = 9.862 m/s at the reference lev... | K + U = constant (conservative systems); U_g = m g h; K = (1/2) m v^2 | newton_second_law; work-energy theorem | Apply conservation of mechanical energy to free-fall motion. |
2,213 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 23.98 m, speed 33.98 m/s | An object moves in a circle of radius 23.98 m at constant speed 33.98 m/s. The centripetal acceleration has magnitude a_c = v² / r = 48.15 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
2,214 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 14.18 m, speed 14.6 m/s | An object moves in a circle of radius 14.18 m at constant speed 14.6 m/s. The centripetal acceleration has magnitude a_c = v² / r = 15.02 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
2,215 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 28.78 m, speed 20.81 m/s | An object moves in a circle of radius 28.78 m at constant speed 20.81 m/s. The centripetal acceleration has magnitude a_c = v² / r = 15.05 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
2,216 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 20.34 m, speed 28.86 m/s | An object moves in a circle of radius 20.34 m at constant speed 28.86 m/s. The centripetal acceleration has magnitude a_c = v² / r = 40.93 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
2,217 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 5.438 m, speed 22.69 m/s | An object moves in a circle of radius 5.438 m at constant speed 22.69 m/s. The centripetal acceleration has magnitude a_c = v² / r = 94.67 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
2,218 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 3.639 m, speed 12.78 m/s | An object moves in a circle of radius 3.639 m at constant speed 12.78 m/s. The centripetal acceleration has magnitude a_c = v² / r = 44.9 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
2,219 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 23.1 m, speed 24.03 m/s | An object moves in a circle of radius 23.1 m at constant speed 24.03 m/s. The centripetal acceleration has magnitude a_c = v² / r = 25 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
2,220 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 12 m, speed 10.5 m/s | An object moves in a circle of radius 12 m at constant speed 10.5 m/s. The centripetal acceleration has magnitude a_c = v² / r = 9.191 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
2,221 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 8.035 m, speed 19.81 m/s | An object moves in a circle of radius 8.035 m at constant speed 19.81 m/s. The centripetal acceleration has magnitude a_c = v² / r = 48.85 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
2,222 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 3.396 m, speed 9.121 m/s | An object moves in a circle of radius 3.396 m at constant speed 9.121 m/s. The centripetal acceleration has magnitude a_c = v² / r = 24.5 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
2,223 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 34.73 m, speed 17.81 m/s | An object moves in a circle of radius 34.73 m at constant speed 17.81 m/s. The centripetal acceleration has magnitude a_c = v² / r = 9.137 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
2,224 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 49.01 m, speed 23.12 m/s | An object moves in a circle of radius 49.01 m at constant speed 23.12 m/s. The centripetal acceleration has magnitude a_c = v² / r = 10.91 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
2,225 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 17.18 m, speed 28.07 m/s | An object moves in a circle of radius 17.18 m at constant speed 28.07 m/s. The centripetal acceleration has magnitude a_c = v² / r = 45.88 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
2,226 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 8.737 m, speed 27.11 m/s | An object moves in a circle of radius 8.737 m at constant speed 27.11 m/s. The centripetal acceleration has magnitude a_c = v² / r = 84.15 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
2,227 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 36.99 m, speed 28.76 m/s | An object moves in a circle of radius 36.99 m at constant speed 28.76 m/s. The centripetal acceleration has magnitude a_c = v² / r = 22.37 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
2,228 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 41.85 m, speed 5.459 m/s | An object moves in a circle of radius 41.85 m at constant speed 5.459 m/s. The centripetal acceleration has magnitude a_c = v² / r = 0.7119 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
2,229 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 29.84 m, speed 13.69 m/s | An object moves in a circle of radius 29.84 m at constant speed 13.69 m/s. The centripetal acceleration has magnitude a_c = v² / r = 6.28 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
2,230 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 4.973 m, speed 18.36 m/s | An object moves in a circle of radius 4.973 m at constant speed 18.36 m/s. The centripetal acceleration has magnitude a_c = v² / r = 67.81 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
2,231 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 15.47 m, speed 16.83 m/s | An object moves in a circle of radius 15.47 m at constant speed 16.83 m/s. The centripetal acceleration has magnitude a_c = v² / r = 18.3 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
2,232 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 29.95 m, speed 27.73 m/s | An object moves in a circle of radius 29.95 m at constant speed 27.73 m/s. The centripetal acceleration has magnitude a_c = v² / r = 25.68 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
2,233 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 29.86 m, speed 32.97 m/s | An object moves in a circle of radius 29.86 m at constant speed 32.97 m/s. The centripetal acceleration has magnitude a_c = v² / r = 36.41 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
2,234 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 16.44 m, speed 26.15 m/s | An object moves in a circle of radius 16.44 m at constant speed 26.15 m/s. The centripetal acceleration has magnitude a_c = v² / r = 41.62 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
2,235 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 3.168 m, speed 9.487 m/s | An object moves in a circle of radius 3.168 m at constant speed 9.487 m/s. The centripetal acceleration has magnitude a_c = v² / r = 28.41 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
2,236 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 7.032 m, speed 23.65 m/s | An object moves in a circle of radius 7.032 m at constant speed 23.65 m/s. The centripetal acceleration has magnitude a_c = v² / r = 79.54 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
2,237 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 37.77 m, speed 32.58 m/s | An object moves in a circle of radius 37.77 m at constant speed 32.58 m/s. The centripetal acceleration has magnitude a_c = v² / r = 28.11 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
2,238 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 37.88 m, speed 26.77 m/s | An object moves in a circle of radius 37.88 m at constant speed 26.77 m/s. The centripetal acceleration has magnitude a_c = v² / r = 18.93 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
2,239 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 22.7 m, speed 12.37 m/s | An object moves in a circle of radius 22.7 m at constant speed 12.37 m/s. The centripetal acceleration has magnitude a_c = v² / r = 6.738 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
2,240 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 30.82 m, speed 18.44 m/s | An object moves in a circle of radius 30.82 m at constant speed 18.44 m/s. The centripetal acceleration has magnitude a_c = v² / r = 11.03 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
2,241 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 10.36 m, speed 35.22 m/s | An object moves in a circle of radius 10.36 m at constant speed 35.22 m/s. The centripetal acceleration has magnitude a_c = v² / r = 119.7 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
2,242 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 15.06 m, speed 31.98 m/s | An object moves in a circle of radius 15.06 m at constant speed 31.98 m/s. The centripetal acceleration has magnitude a_c = v² / r = 67.92 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
2,243 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 34.01 m, speed 36.82 m/s | An object moves in a circle of radius 34.01 m at constant speed 36.82 m/s. The centripetal acceleration has magnitude a_c = v² / r = 39.87 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
2,244 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 46.84 m, speed 28.99 m/s | An object moves in a circle of radius 46.84 m at constant speed 28.99 m/s. The centripetal acceleration has magnitude a_c = v² / r = 17.95 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
2,245 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 45.76 m, speed 39.62 m/s | An object moves in a circle of radius 45.76 m at constant speed 39.62 m/s. The centripetal acceleration has magnitude a_c = v² / r = 34.3 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
2,246 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 29.18 m, speed 24.85 m/s | An object moves in a circle of radius 29.18 m at constant speed 24.85 m/s. The centripetal acceleration has magnitude a_c = v² / r = 21.16 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
2,247 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 25.57 m, speed 34.06 m/s | An object moves in a circle of radius 25.57 m at constant speed 34.06 m/s. The centripetal acceleration has magnitude a_c = v² / r = 45.36 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
2,248 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 42.64 m, speed 3.434 m/s | An object moves in a circle of radius 42.64 m at constant speed 3.434 m/s. The centripetal acceleration has magnitude a_c = v² / r = 0.2766 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
2,249 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 45.06 m, speed 38.75 m/s | An object moves in a circle of radius 45.06 m at constant speed 38.75 m/s. The centripetal acceleration has magnitude a_c = v² / r = 33.32 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
2,250 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 0.1421 m, speed 22.84 m/s | An object moves in a circle of radius 0.1421 m at constant speed 22.84 m/s. The centripetal acceleration has magnitude a_c = v² / r = 3672 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
2,251 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 48.94 m, speed 5.278 m/s | An object moves in a circle of radius 48.94 m at constant speed 5.278 m/s. The centripetal acceleration has magnitude a_c = v² / r = 0.5693 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
2,252 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 14.18 m, speed 2.216 m/s | An object moves in a circle of radius 14.18 m at constant speed 2.216 m/s. The centripetal acceleration has magnitude a_c = v² / r = 0.3463 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
2,253 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 21.64 m, speed 24.02 m/s | An object moves in a circle of radius 21.64 m at constant speed 24.02 m/s. The centripetal acceleration has magnitude a_c = v² / r = 26.65 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
2,254 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 31.3 m, speed 28.76 m/s | An object moves in a circle of radius 31.3 m at constant speed 28.76 m/s. The centripetal acceleration has magnitude a_c = v² / r = 26.43 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
2,255 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 20.36 m, speed 17.97 m/s | An object moves in a circle of radius 20.36 m at constant speed 17.97 m/s. The centripetal acceleration has magnitude a_c = v² / r = 15.86 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
2,256 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 10.64 m, speed 7.763 m/s | An object moves in a circle of radius 10.64 m at constant speed 7.763 m/s. The centripetal acceleration has magnitude a_c = v² / r = 5.664 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
2,257 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 7.04 m, speed 22.66 m/s | An object moves in a circle of radius 7.04 m at constant speed 22.66 m/s. The centripetal acceleration has magnitude a_c = v² / r = 72.95 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
2,258 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 42.18 m, speed 15.05 m/s | An object moves in a circle of radius 42.18 m at constant speed 15.05 m/s. The centripetal acceleration has magnitude a_c = v² / r = 5.371 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
2,259 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 20.92 m, speed 12.25 m/s | An object moves in a circle of radius 20.92 m at constant speed 12.25 m/s. The centripetal acceleration has magnitude a_c = v² / r = 7.174 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
2,260 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 43.65 m, speed 5.896 m/s | An object moves in a circle of radius 43.65 m at constant speed 5.896 m/s. The centripetal acceleration has magnitude a_c = v² / r = 0.7965 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
2,261 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 0.679 m, speed 26.29 m/s | An object moves in a circle of radius 0.679 m at constant speed 26.29 m/s. The centripetal acceleration has magnitude a_c = v² / r = 1018 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
2,262 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 7.285 m, speed 35.51 m/s | An object moves in a circle of radius 7.285 m at constant speed 35.51 m/s. The centripetal acceleration has magnitude a_c = v² / r = 173.1 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
2,263 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 32.93 m, speed 39.02 m/s | An object moves in a circle of radius 32.93 m at constant speed 39.02 m/s. The centripetal acceleration has magnitude a_c = v² / r = 46.25 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
2,264 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 6.875 m, speed 6.352 m/s | An object moves in a circle of radius 6.875 m at constant speed 6.352 m/s. The centripetal acceleration has magnitude a_c = v² / r = 5.868 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
2,265 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 40.32 m, speed 34.55 m/s | An object moves in a circle of radius 40.32 m at constant speed 34.55 m/s. The centripetal acceleration has magnitude a_c = v² / r = 29.6 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
2,266 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 44.69 m, speed 28.12 m/s | An object moves in a circle of radius 44.69 m at constant speed 28.12 m/s. The centripetal acceleration has magnitude a_c = v² / r = 17.69 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
2,267 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 46.52 m, speed 25.31 m/s | An object moves in a circle of radius 46.52 m at constant speed 25.31 m/s. The centripetal acceleration has magnitude a_c = v² / r = 13.77 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
2,268 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 22.77 m, speed 17.54 m/s | An object moves in a circle of radius 22.77 m at constant speed 17.54 m/s. The centripetal acceleration has magnitude a_c = v² / r = 13.51 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
2,269 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 41.02 m, speed 16 m/s | An object moves in a circle of radius 41.02 m at constant speed 16 m/s. The centripetal acceleration has magnitude a_c = v² / r = 6.244 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
2,270 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 11.36 m, speed 17.57 m/s | An object moves in a circle of radius 11.36 m at constant speed 17.57 m/s. The centripetal acceleration has magnitude a_c = v² / r = 27.15 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
2,271 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 0.4708 m, speed 20.43 m/s | An object moves in a circle of radius 0.4708 m at constant speed 20.43 m/s. The centripetal acceleration has magnitude a_c = v² / r = 886.5 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
2,272 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 36.57 m, speed 28.77 m/s | An object moves in a circle of radius 36.57 m at constant speed 28.77 m/s. The centripetal acceleration has magnitude a_c = v² / r = 22.64 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
2,273 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 13.54 m, speed 37.14 m/s | An object moves in a circle of radius 13.54 m at constant speed 37.14 m/s. The centripetal acceleration has magnitude a_c = v² / r = 101.9 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
2,274 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 28.86 m, speed 2.305 m/s | An object moves in a circle of radius 28.86 m at constant speed 2.305 m/s. The centripetal acceleration has magnitude a_c = v² / r = 0.1841 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
2,275 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 1.989 m, speed 19.85 m/s | An object moves in a circle of radius 1.989 m at constant speed 19.85 m/s. The centripetal acceleration has magnitude a_c = v² / r = 198 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
2,276 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 18.49 m, speed 23.63 m/s | An object moves in a circle of radius 18.49 m at constant speed 23.63 m/s. The centripetal acceleration has magnitude a_c = v² / r = 30.2 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
2,277 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 48.09 m, speed 4.122 m/s | An object moves in a circle of radius 48.09 m at constant speed 4.122 m/s. The centripetal acceleration has magnitude a_c = v² / r = 0.3534 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
2,278 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 36.54 m, speed 21.53 m/s | An object moves in a circle of radius 36.54 m at constant speed 21.53 m/s. The centripetal acceleration has magnitude a_c = v² / r = 12.69 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
2,279 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 42.98 m, speed 30.27 m/s | An object moves in a circle of radius 42.98 m at constant speed 30.27 m/s. The centripetal acceleration has magnitude a_c = v² / r = 21.32 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
2,280 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 14.04 m, speed 21.16 m/s | An object moves in a circle of radius 14.04 m at constant speed 21.16 m/s. The centripetal acceleration has magnitude a_c = v² / r = 31.89 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
2,281 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 26.22 m, speed 24.79 m/s | An object moves in a circle of radius 26.22 m at constant speed 24.79 m/s. The centripetal acceleration has magnitude a_c = v² / r = 23.45 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
2,282 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 12.34 m, speed 25.6 m/s | An object moves in a circle of radius 12.34 m at constant speed 25.6 m/s. The centripetal acceleration has magnitude a_c = v² / r = 53.1 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
2,283 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 33.22 m, speed 27.08 m/s | An object moves in a circle of radius 33.22 m at constant speed 27.08 m/s. The centripetal acceleration has magnitude a_c = v² / r = 22.07 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
2,284 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 34.24 m, speed 22.03 m/s | An object moves in a circle of radius 34.24 m at constant speed 22.03 m/s. The centripetal acceleration has magnitude a_c = v² / r = 14.17 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
2,285 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 29.02 m, speed 24.91 m/s | An object moves in a circle of radius 29.02 m at constant speed 24.91 m/s. The centripetal acceleration has magnitude a_c = v² / r = 21.38 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
2,286 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 45.19 m, speed 21.87 m/s | An object moves in a circle of radius 45.19 m at constant speed 21.87 m/s. The centripetal acceleration has magnitude a_c = v² / r = 10.58 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
2,287 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 0.6381 m, speed 18.71 m/s | An object moves in a circle of radius 0.6381 m at constant speed 18.71 m/s. The centripetal acceleration has magnitude a_c = v² / r = 548.5 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
2,288 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 45.31 m, speed 23.38 m/s | An object moves in a circle of radius 45.31 m at constant speed 23.38 m/s. The centripetal acceleration has magnitude a_c = v² / r = 12.07 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
2,289 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 16.64 m, speed 14.76 m/s | An object moves in a circle of radius 16.64 m at constant speed 14.76 m/s. The centripetal acceleration has magnitude a_c = v² / r = 13.1 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
2,290 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 48.89 m, speed 12.49 m/s | An object moves in a circle of radius 48.89 m at constant speed 12.49 m/s. The centripetal acceleration has magnitude a_c = v² / r = 3.191 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
2,291 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 8.459 m, speed 28.11 m/s | An object moves in a circle of radius 8.459 m at constant speed 28.11 m/s. The centripetal acceleration has magnitude a_c = v² / r = 93.4 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
2,292 | physics | mechanics | uniform_circular_motion | 5 | worked_example | Centripetal acceleration: radius 29.92 m, speed 12.86 m/s | An object moves in a circle of radius 29.92 m at constant speed 12.86 m/s. The centripetal acceleration has magnitude a_c = v² / r = 5.526 m/s² and is directed toward the center of the circle. The corresponding centripetal force is supplied by whatever agent constrains the motion (tension, gravity, friction, etc.). | a_c = v^2 / r; F_c = m v^2 / r | newton_second_law | Calculate centripetal acceleration and identify the force providing it. |
2,293 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 6.2356e-05 C and 5.7856e-04 C separated by 1.15 m | Two point charges q1 = 6.2356e-05 C and q2 = 5.7856e-04 C are separated by distance r = 1.15 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 245.2 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
2,294 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 8.0909e-04 C and -2.8753e-04 C separated by 0.1742 m | Two point charges q1 = 8.0909e-04 C and q2 = -2.8753e-04 C are separated by distance r = 0.1742 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 6.8904e+04 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
2,295 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -8.5159e-04 C and 2.5280e-04 C separated by 1.235 m | Two point charges q1 = -8.5159e-04 C and q2 = 2.5280e-04 C are separated by distance r = 1.235 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1268 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
2,296 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 8.5800e-04 C and -7.4169e-04 C separated by 1.212 m | Two point charges q1 = 8.5800e-04 C and q2 = -7.4169e-04 C are separated by distance r = 1.212 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 3896 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
2,297 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -6.5950e-04 C and 8.0803e-04 C separated by 0.5299 m | Two point charges q1 = -6.5950e-04 C and q2 = 8.0803e-04 C are separated by distance r = 0.5299 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1.7057e+04 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
2,298 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -4.8543e-04 C and -3.4351e-04 C separated by 0.178 m | Two point charges q1 = -4.8543e-04 C and q2 = -3.4351e-04 C are separated by distance r = 0.178 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 4.7322e+04 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
2,299 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges -5.9595e-04 C and -8.3778e-04 C separated by 1.508 m | Two point charges q1 = -5.9595e-04 C and q2 = -8.3778e-04 C are separated by distance r = 1.508 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 1973 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
2,300 | physics | electromagnetism | coulomb_law | 5 | worked_example | Coulomb force between charges 7.7060e-04 C and -6.6101e-04 C separated by 1.455 m | Two point charges q1 = 7.7060e-04 C and q2 = -6.6101e-04 C are separated by distance r = 1.455 m in vacuum. The magnitude of the electrostatic force is F = k |q1 q2| / r² = 2163 N, where k = 8.9875517923 × 10⁹ N·m²/C². The force is repulsive if the charges have the same sign and attractive if opposite. | F = k |q1 q2| / r^2; k = 1/(4 π ε_0) | newton_second_law | Compute the Coulomb force between two point charges. |
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