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Simple machines are devices that can be used to multiply or augment a force that we apply â often at the expense of a distance through which we have to apply the force. | https://openstax.org/books/college-physics-2e/pages/9-section-summary |
The ratio of output to input forces for any simple machine is called its mechanical advantage | https://openstax.org/books/college-physics-2e/pages/9-section-summary |
A few simple machines are the lever, nail puller, wheelbarrow, crank, etc. | https://openstax.org/books/college-physics-2e/pages/9-section-summary |
Statics plays an important part in understanding everyday strains in our muscles and bones. | https://openstax.org/books/college-physics-2e/pages/9-section-summary |
Many lever systems in the body have a mechanical advantage of significantly less than one, as many of our muscles are attached close to joints. | https://openstax.org/books/college-physics-2e/pages/9-section-summary |
Someone with good posture stands or sits in such a way that the person's center of gravity lies directly above the pivot point in the hips, thereby avoiding back strain and damage to disks. | https://openstax.org/books/college-physics-2e/pages/9-section-summary |
angular acceleration : the rate of change of angular velocity with time | https://openstax.org/books/college-physics-2e/pages/10-glossary |
angular momentum : the product of moment of inertia and angular velocity | https://openstax.org/books/college-physics-2e/pages/10-glossary |
change in angular velocity : the difference between final and initial values of angular velocity | https://openstax.org/books/college-physics-2e/pages/10-glossary |
kinematics of rotational motion : describes the relationships among rotation angle, angular velocity, angular acceleration, and time | https://openstax.org/books/college-physics-2e/pages/10-glossary |
law of conservation of angular momentum : angular momentum is conserved, i.e., the initial angular momentum is equal to the final angular momentum when no external torque is applied to the system | https://openstax.org/books/college-physics-2e/pages/10-glossary |
moment of inertia : mass times the square of perpendicular distance from the rotation axis; for a point mass, it isI=mr2I=mr2and, because any object can be built up from a collection of point masses, this relationship is the basis for all other moments of inertia | https://openstax.org/books/college-physics-2e/pages/10-glossary |
right-hand rule : direction of angular velocity Ï and angular momentum L in which the thumb of your right hand points when you curl your fingers in the direction of the diskâs rotation | https://openstax.org/books/college-physics-2e/pages/10-glossary |
rotational inertia : resistance to change of rotation. The more rotational inertia an object has, the harder it is to rotate | https://openstax.org/books/college-physics-2e/pages/10-glossary |
rotational kinetic energy : the kinetic energy due to the rotation of an object. This is part of its total kinetic energy | https://openstax.org/books/college-physics-2e/pages/10-glossary |
tangential acceleration : the acceleration in a direction tangent to the circle at the point of interest in circular motion | https://openstax.org/books/college-physics-2e/pages/10-glossary |
torque : the turning effectiveness of a force | https://openstax.org/books/college-physics-2e/pages/10-glossary |
work-energy theorem : if one or more external forces act upon a rigid object, causing its kinetic energy to change fromKE1KE1toKE2KE2, then the workWWdone by the net force is equal to the change in kinetic energy | https://openstax.org/books/college-physics-2e/pages/10-glossary |
Uniform circular motion is the motion with a constant angular velocityÏ=ÎθÎtÏ=ÎθÎt. | https://openstax.org/books/college-physics-2e/pages/10-section-summary |
In non-uniform circular motion, the velocity changes with time and the rate of change of angular velocity (i.e. angular acceleration) isα=ÎÏÎtα=ÎÏÎt. | https://openstax.org/books/college-physics-2e/pages/10-section-summary |
Linear or tangential acceleration refers to changes in the magnitude of velocity but not its direction, given asat=ÎvÎtat=ÎvÎt. | https://openstax.org/books/college-physics-2e/pages/10-section-summary |
For circular motion, note thatv=rÏv=rÏ, so thatat=ÎrÏÎt.at=ÎrÏÎt. | https://openstax.org/books/college-physics-2e/pages/10-section-summary |
The radius r is constant for circular motion, and soÎrÏ=rÎÏÎrÏ=rÎÏ. Thus,at=rÎÏÎt.at=rÎÏÎt. | https://openstax.org/books/college-physics-2e/pages/10-section-summary |
By definition,ÎÏ/Ît=αÎÏ/Ît=α. Thus,at=rαat=rαorα=atr.α=atr. | https://openstax.org/books/college-physics-2e/pages/10-section-summary |
or | https://openstax.org/books/college-physics-2e/pages/10-section-summary |
Kinematics is the description of motion. | https://openstax.org/books/college-physics-2e/pages/10-section-summary |
The kinematics of rotational motion describes the relationships among rotation angle, angular velocity, angular acceleration, and time. | https://openstax.org/books/college-physics-2e/pages/10-section-summary |
Starting with the four kinematic equations we developed in theOne-Dimensional Kinematics, we can derive the four rotational kinematic equations (presented together with their translational counterparts) seen inTable 10.2. | https://openstax.org/books/college-physics-2e/pages/10-section-summary |
In these equations, the subscript 0 denotes initial values (x0x0andt0t0are initial values), and the average angular velocityÏ-Ï-and average velocityv-v-are defined as follows:ϯ=Ï0+Ï2andv¯=v0+v2.ϯ=Ï0+Ï2andv¯=v0+v2. | https://openstax.org/books/college-physics-2e/pages/10-section-summary |
The farther the force is applied from the pivot, the greater is the angular acceleration; angular acceleration is inversely proportional to mass. | https://openstax.org/books/college-physics-2e/pages/10-section-summary |
If we exert a forceFFon a point massmmthat is at a distancerrfrom a pivot point and because the force is perpendicular torr, an accelerationa = F/ma = F/mis obtained in the direction ofFF. We can rearrange this equation such thatF = ma,F = ma,and then look for ways to relate this expression to expressions for rotationa... | https://openstax.org/books/college-physics-2e/pages/10-section-summary |
and then look for ways to relate this expression to expressions for rotational quantities. We note thata = rαa = rα, and we substitute this expression intoF=maF=ma, yielding | https://openstax.org/books/college-physics-2e/pages/10-section-summary |
Torque is the turning effectiveness of a force. In this case, becauseFFis perpendicular torr, torque is simplyÏ=rFÏ=rF. If we multiply both sides of the equation above byrr, we get torque on the left-hand side. That is,rF=mr2αrF=mr2αorÏ=mr2α.Ï=mr2α. | https://openstax.org/books/college-physics-2e/pages/10-section-summary |
or | https://openstax.org/books/college-physics-2e/pages/10-section-summary |
The moment of inertiaIIof an object is the sum ofMR2MR2for all the point masses of which it is composed. That is,I=âmr2.I=âmr2. | https://openstax.org/books/college-physics-2e/pages/10-section-summary |
The general relationship among torque, moment of inertia, and angular acceleration isÏ=IαÏ=Iαorα=net ÏIâα=net ÏIâ | https://openstax.org/books/college-physics-2e/pages/10-section-summary |
or | https://openstax.org/books/college-physics-2e/pages/10-section-summary |
The rotational kinetic energyKErotKErotfor an object with a moment of inertiaIIand an angular velocityÏÏis given byKErot=12IÏ2.KErot=12IÏ2. | https://openstax.org/books/college-physics-2e/pages/10-section-summary |
Helicopters store large amounts of rotational kinetic energy in their blades. This energy must be put into the blades before takeoff and maintained until the end of the flight. The engines do not have enough power to simultaneously provide lift and put significant rotational energy into the blades. | https://openstax.org/books/college-physics-2e/pages/10-section-summary |
Work and energy in rotational motion are completely analogous to work and energy in translational motion. | https://openstax.org/books/college-physics-2e/pages/10-section-summary |
The equation for thework-energy theoremfor rotational motion is,netW=12IÏ2â12IÏ02.netW=12IÏ2â12IÏ02. | https://openstax.org/books/college-physics-2e/pages/10-section-summary |
Every rotational phenomenon has a direct translational analog , likewise angular momentumLLcan be defined asL=IÏ.L=IÏ. | https://openstax.org/books/college-physics-2e/pages/10-section-summary |
This equation is an analog to the definition of linear momentum asp=mvp=mv. The relationship between torque and angular momentum isnetÏ=ÎLÎt.netÏ=ÎLÎt. | https://openstax.org/books/college-physics-2e/pages/10-section-summary |
Angular momentum, like energy and linear momentum, is conserved. This universally applicable law is another sign of underlying unity in physical laws. Angular momentum is conserved when net external torque is zero, just as linear momentum is conserved when the net external force is zero. | https://openstax.org/books/college-physics-2e/pages/10-section-summary |
Angular momentumLLis analogous to linear momentum and is given byL=IÏL=IÏ. | https://openstax.org/books/college-physics-2e/pages/10-section-summary |
Angular momentum is changed by torque, following the relationshipnetÏ=ÎLÎt.netÏ=ÎLÎt. | https://openstax.org/books/college-physics-2e/pages/10-section-summary |
Angular momentum is conserved if the net torque is zeroL=constantnetÏ=0L=constantnetÏ=0orL=Lâ²netÏ=0L=Lâ²netÏ=0. This equation is known as the law of conservation of angular momentum, which may be conserved in collisions. | https://openstax.org/books/college-physics-2e/pages/10-section-summary |
Torque is perpendicular to the plane formed byrrandFFand is the direction your right thumb would point if you curled the fingers of your right hand in the direction ofFF. The direction of the torque is thus the same as that of the angular momentum it produces. | https://openstax.org/books/college-physics-2e/pages/10-section-summary |
The gyroscope precesses around a vertical axis, since the torque is always horizontal and perpendicular toLL. If the gyroscope is not spinning, it acquires angular momentum in the direction of the torque (L=ÎLL=ÎL), and it rotates about a horizontal axis, falling over just as we would expect. | https://openstax.org/books/college-physics-2e/pages/10-section-summary |
Earth itself acts like a gigantic gyroscope. Its angular momentum is along its axis and points at Polaris, the North Star. | https://openstax.org/books/college-physics-2e/pages/10-section-summary |
absolute pressure : the sum of gauge pressure and atmospheric pressure | https://openstax.org/books/college-physics-2e/pages/11-glossary |
adhesive forces : the attractive forces between molecules of different types | https://openstax.org/books/college-physics-2e/pages/11-glossary |
Archimedesâ principle : the buoyant force on an object equals the weight of the fluid it displaces | https://openstax.org/books/college-physics-2e/pages/11-glossary |
buoyant force : the net upward force on any object in any fluid | https://openstax.org/books/college-physics-2e/pages/11-glossary |
capillary action : the tendency of a fluid to be raised or lowered in a narrow tube | https://openstax.org/books/college-physics-2e/pages/11-glossary |
cohesive forces : the attractive forces between molecules of the same type | https://openstax.org/books/college-physics-2e/pages/11-glossary |
contact angle : the angleθθbetween the tangent to the liquid surface and the surface | https://openstax.org/books/college-physics-2e/pages/11-glossary |
density : the mass per unit volume of a substance or object | https://openstax.org/books/college-physics-2e/pages/11-glossary |
diastolic pressure : minimum arterial blood pressure; indicator for the fluid balance | https://openstax.org/books/college-physics-2e/pages/11-glossary |
diastolic pressure : the minimum blood pressure in the artery | https://openstax.org/books/college-physics-2e/pages/11-glossary |
fluids : liquids and gases; a fluid is a state of matter that yields to shearing forces | https://openstax.org/books/college-physics-2e/pages/11-glossary |
gauge pressure : the pressure relative to atmospheric pressure | https://openstax.org/books/college-physics-2e/pages/11-glossary |
glaucoma : condition caused by the buildup of fluid pressure in the eye | https://openstax.org/books/college-physics-2e/pages/11-glossary |
intraocular pressure : fluid pressure in the eye | https://openstax.org/books/college-physics-2e/pages/11-glossary |
micturition reflex : stimulates the feeling of needing to urinate, triggered by bladder pressure | https://openstax.org/books/college-physics-2e/pages/11-glossary |
Pascalâs Principle : a change in pressure applied to an enclosed fluid is transmitted undiminished to all portions of the fluid and to the walls of its container | https://openstax.org/books/college-physics-2e/pages/11-glossary |
pressure : the force per unit area perpendicular to the force, over which the force acts | https://openstax.org/books/college-physics-2e/pages/11-glossary |
pressure : the weight of the fluid divided by the area supporting it | https://openstax.org/books/college-physics-2e/pages/11-glossary |
specific gravity : the ratio of the density of an object to a fluid (usually water) | https://openstax.org/books/college-physics-2e/pages/11-glossary |
surface tension : the cohesive forces between molecules which cause the surface of a liquid to contract to the smallest possible surface area | https://openstax.org/books/college-physics-2e/pages/11-glossary |
systolic pressure : maximum arterial blood pressure; indicator for the blood flow | https://openstax.org/books/college-physics-2e/pages/11-glossary |
systolic pressure : the maximum blood pressure in the artery | https://openstax.org/books/college-physics-2e/pages/11-glossary |
A fluid is a state of matter that yields to sideways or shearing forces. Liquids and gases are both fluids. Fluid statics is the physics of stationary fluids. | https://openstax.org/books/college-physics-2e/pages/11-section-summary |
Density is the mass per unit volume of a substance or object. In equation form, density is defined asÏ=mV.Ï=mV. | https://openstax.org/books/college-physics-2e/pages/11-section-summary |
The SI unit of density iskg/m3kg/m3. | https://openstax.org/books/college-physics-2e/pages/11-section-summary |
Pressure is the force per unit perpendicular area over which the force is applied. In equation form, pressure is defined asP=FA.P=FA. | https://openstax.org/books/college-physics-2e/pages/11-section-summary |
The SI unit of pressure is pascal and1 Pa=1N/m21 Pa=1N/m2. | https://openstax.org/books/college-physics-2e/pages/11-section-summary |
Pressure is the weight of the fluidmgmgdivided by the areaAAsupporting it (the area of the bottom of the container):P=mgA.P=mgA. | https://openstax.org/books/college-physics-2e/pages/11-section-summary |
Pressure due to the weight of a liquid is given byP=hÏg,P=hÏg,wherePPis the pressure,hhis the height of the liquid,ÏÏis the density of the liquid, andggis the acceleration due to gravity. | https://openstax.org/books/college-physics-2e/pages/11-section-summary |
wherePPis the pressure,hhis the height of the liquid,ÏÏis the density of the liquid, andggis the acceleration due to gravity. | https://openstax.org/books/college-physics-2e/pages/11-section-summary |
Pressure is force per unit area. | https://openstax.org/books/college-physics-2e/pages/11-section-summary |
A change in pressure applied to an enclosed fluid is transmitted undiminished to all portions of the fluid and to the walls of its container. | https://openstax.org/books/college-physics-2e/pages/11-section-summary |
A hydraulic system is an enclosed fluid system used to exert forces. | https://openstax.org/books/college-physics-2e/pages/11-section-summary |
Gauge pressure is the pressure relative to atmospheric pressure. | https://openstax.org/books/college-physics-2e/pages/11-section-summary |
Absolute pressure is the sum of gauge pressure and atmospheric pressure. | https://openstax.org/books/college-physics-2e/pages/11-section-summary |
Aneroid gauge measures pressure using a bellows-and-spring arrangement connected to the pointer of a calibrated scale. | https://openstax.org/books/college-physics-2e/pages/11-section-summary |
Open-tube manometers have U-shaped tubes and one end is always open. It is used to measure pressure. | https://openstax.org/books/college-physics-2e/pages/11-section-summary |
A mercury barometer is a device that measures atmospheric pressure. | https://openstax.org/books/college-physics-2e/pages/11-section-summary |
Buoyant force is the net upward force on any object in any fluid. If the buoyant force is greater than the objectâs weight, the object will rise to the surface and float. If the buoyant force is less than the objectâs weight, the object will sink. If the buoyant force equals the objectâs weight, the object will r... | https://openstax.org/books/college-physics-2e/pages/11-section-summary |
Archimedesâ principle states that the buoyant force on an object equals the weight of the fluid it displaces. | https://openstax.org/books/college-physics-2e/pages/11-section-summary |
Specific gravity is the ratio of the density of an object to a fluid (usually water). | https://openstax.org/books/college-physics-2e/pages/11-section-summary |
Attractive forces between molecules of the same type are called cohesive forces. | https://openstax.org/books/college-physics-2e/pages/11-section-summary |
Attractive forces between molecules of different types are called adhesive forces. | https://openstax.org/books/college-physics-2e/pages/11-section-summary |
Cohesive forces between molecules cause the surface of a liquid to contract to the smallest possible surface area. This general effect is called surface tension. | https://openstax.org/books/college-physics-2e/pages/11-section-summary |
Capillary action is the tendency of a fluid to be raised or suppressed in a narrow tube, or capillary tube which is due to the relative strength of cohesive and adhesive forces. | https://openstax.org/books/college-physics-2e/pages/11-section-summary |
Measuring blood pressure is among the most common of all medical examinations. | https://openstax.org/books/college-physics-2e/pages/11-section-summary |
The pressures in various parts of the body can be measured and often provide valuable medical indicators. | https://openstax.org/books/college-physics-2e/pages/11-section-summary |
The shape of the eye is maintained by fluid pressure, called intraocular pressure. | https://openstax.org/books/college-physics-2e/pages/11-section-summary |
When the circulation of fluid in the eye is blocked, it can lead to a buildup in pressure, a condition called glaucoma. | https://openstax.org/books/college-physics-2e/pages/11-section-summary |
Some of the other pressures in the body are spinal and skull pressures, bladder pressure, pressures in the skeletal system. | https://openstax.org/books/college-physics-2e/pages/11-section-summary |
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