knowledge.txt

[SYSTEM_INSTRUCTION]
- You are an expert Physics tutor bot.
- Always provide step-by-step solutions (Identify, Formula, Calculation, Result).
- Use LaTeX format for formulas.
- If a problem is ambiguous, ask for clarification.
- Convert all units to SI (Systeme International) before calculating.

[CORE_TOPICS]
- Equations of Motion & Dynamics (Forces, Newton's Laws)
- Thermodynamics & Statistical Mechanics
- Electromagnetism (Maxwell's Equations)
- Quantum Mechanics (Schrödinger Equation)
- Optics & Waves
- Light 

[DEFINITIONS]
// Equations of Motion: Specific Equations for an object moving in a straight line with constant acceleration.
Variables in the Equations of Motion: u = initial velocity; v = final velocity; a = acceleration; t = time; s = displacement.  

// Properties of Light: 
1. It is a form of energy 
2. It travels in straight lines at a speed of 3.00 x 10^8 m/s
3. It can be reflected 
4. It can be refracted 
5. It can be dispersed 
6. It can be diffracted 
7. It can be polorised 
8. It can undergo interference

Reflection : bouncing of light off a surface 

[FORMULA_SHEET]
// Equations of Motion
v = u + at
s = ut + 0.5at^2
v^2 = u^2 + 2as

// Dynamics
F = ma
F_f = μN (Friction)

// Energy & Work
W = Fd cos(θ)
KE = 0.5mv^2
PE = mgh
E_total = KE + PE

// Electromagnetism
F = k(q1q2)/r^2 (Coulomb's Law)
V = IR (Ohm's Law)
∇ · E = ρ/ε₀ (Maxwell's Equation 1)

[PROBLEM_SOLVING_ALGORITHM]
1. Read the problem and identify known/unknown variables.
2. Sketch a diagram if necessary.
3. Select the appropriate physical principle or formula.
4. Convert units to SI.
5. Solve for the unknown variable symbolically.
6. Plug in values and compute the result.
7. Verify the units of the answer.

[COMMON_CONSTANTS]
- Speed of light (c): 3.00 x 10^8 m/s
- Planck's constant (h): 6.626 x 10^-34 J·s
- Gravitational constant (G): 6.674 x 10^-11 N·m²/kg²
- Acceleration due to gravity (g): 9.81 m/s²

Physics Terms Definitions and Units 
Ref Item Definition
3.1.1(c) Scalar A scalar is a quantity that has magnitude only.
 Vector A vector is a quantity that has magnitude and
direction.
3.1.1(i) The moment (or
torque) of a force.
The turning effect of a force (or moment or torque)
about a point is defined as the force x the
perpendicular distance from the point to the line of
action of the force, i.e. moment = F × d.
UNIT: Nm.
3.1.1(j) The principle of
moments.
For a system to be in equilibrium, ∑ anticlockwise
moments about a point = ∑ clockwise moments
about the same point.
3.1.1(k) Centre of gravity. The centre of gravity is the single point within a
body at which the entire weight of the body is
considered to act.
Displacement The displacement of a point B from a point A is the
shortest distance from A to B, together with the
direction. UNIT: m.
Mean Speed Mean speed =
total distance travelled /
total time taken
x
t
∆ = ∆
UNIT: ms-1.
Instantaneous Speed instantaneous speed = rate of change of distance
UNIT: ms-1.
Mean Velocity Mean velocity = total displacement /
total time taken
UNIT: ms-1.
Instantaneous
Velocity
The velocity of a body is the rate of change of
displacement.
UNIT: ms-1
Mean Acceleration Mean Acceleration = change in velocity /
time taken
v
t
∆ = ∆
UNIT: ms-2.
Instantaneous
Acceleration
The instantaneous acceleration of a body is its rate
of change of velocity. UNIT: ms-2
3.1.2(a)
Terminal Velocity The terminal velocity is the constant, maximum
velocity of an object when the resistive forces on it
are equal and opposite to the accelerating forces (e.g.
pull of gravity).
Hookeís Law The tension in a spring or wire is proportional to its
extension from its natural length, provided the
extension is not too great.
3.1.3(b)
Spring Constant The spring constant is the force per unit extension.
UNIT: Nm-1.
Physics Terms Definitions and Units page 4
Stress Stress is the force per unit cross-sectional area when
equal opposing forces act on a body.
UNIT: Pa or Nm-2.
Strain Strain is defined as the extension per unit length due
to an applied stress. UNIT: none
3.1.3(c)
The Young
Modulus Young Modulus tensile stress
tensile strain
E =
Unless otherwise indicated this is defined for the
Hookeís Law region. UNIT: Nm-2
Amplitude The amplitude is defined as the maximum
displacement of any particle from its equilibrium
position.
Wavelength of a
progressive wave
The wavelength of a progressive wave is the
minimum distance between two points on the wave
oscillating in phase.
Frequency of a
wave
The frequency of a wave is the number of cycles of a
wave that pass a given point in one second,
or equivalently
The frequency of a wave is the number of cycles of
oscillation performed by any particle in the medium
through which the wave is passing.
3.1.4(d)
Velocity of a wave The velocity of a wave is the distance that the wave
profile moves per unit time.
3.1.4(e) Intensity of a wave Energy per second passing normally through a given area
 Area
Transverse wave A transverse wave is one where the particle
oscillations are at 90° (right angles) to the direction
of travel (or propagation) of the wave.
3.1.4(h)
Longitudinal wave A longitudinal wave is one where the particle
oscillations are in line with (parallel to) the direction
of travel (or propagation) of the wave.
3.1.4(i) The principle of
superposition.
The principle of superposition states that if two or
more waves occupy the same region then the total
displacement at any one point is the vector sum of
their individual displacements at that point.
Coherence Waves or wave sources, which have a constant phase
difference between them (and therefore must have
the same frequency) are said to be coherent.
3.1.4(m)
Phase difference Phase difference is the difference in position of 2
points within a cycle of oscillation measured as a
fraction of the cycle. [Alternatively it can be
expressed as an angle where one whole cycle is
360°]
3.1.5(a) Snellís law At the boundary between any two given materials,
the ratio of the sine of the angle of incidence to the
sine of the angle of refraction is a constant.
Physics Terms Definitions and Units page 5
PH2
Ref. Item Definition
3.2.1(a) Electric current, I. This is the rate of flow of electric charge. I = ∆Q/∆t.
Unit: A
3.2.2(a) Potential difference
(p.d.), V.
The p.d. between two points is the energy converted
from electrical potential energy to some other form
per coulomb of charge flowing from one point to the
other. Unit: volt (V) [= JC-1].
3.2.2(b) e.m.f. The e.m.f. of a source is the energy converted from
some other form (e.g. chemical) to electrical
potential energy per coulomb of charge flowing
through the source. Unit: volt (V) [= JC-1].

3.2.3(b) Ohmís Law. The current flowing through a metal wire at constant
temperature is proportional to the p.d. across it.
3.2.3(d) Electrical
Resistance, R.
The resistance of a conductor is the p.d. (V) placed
across it divided by the resulting current (I) through
it. R = V / I Unit: ohm (Ω) [= VA-1].
3.2.3(f) Resistivity, ρ The resistance, R, of a metal wire of length L and
cross-sectional area A is given by R = ρ L / A, in
which ρ, the resistivity, is a constant (at constant
temperature) for the material of the wire.
Unit: ohm-metre (Ωm)
3.2.3(h) Temperature
coefficient of
resistance, α.
If the resistance of a conductor at 0°C is R0 and its
resistance at θ °C is Rθ then α is defined by:
α = (Rθ ñ R0 ) / R0θ . [It is the fractional change in
resistance per degree rise in temperature above 0°C.]
Unit: °C-1

3.2.4(a) The Law of
Conservation of
Charge.
Electric charge cannot be created or destroyed,
(though positive and negative charges can neutralize
each other). In a purely resistive circuit charge
cannot pile up at a point.

Nucleon. Protons and neutrons have similar masses. They are
both classed as ënucleonsí.
Atomic mass
number, A
The atomic mass number of an atom is the number
of nucleons (number of protons + number of
neutrons) in its nucleus.
3.2.5(b)
Atomic number, Z. The atomic number of an atom is the number of
protons in its nucleus. [This determines the chemical
element which the atom represents.]
3.2.5(c) Nuclide A nuclide is a particular variety of nucleus, that is a
nucleus with a particular A and Z.
3.2.5(d) Isotope. Isotopes are atoms with the same number of protons,
but different numbers of neutrons in their nuclei.
Physics Terms Definitions and Units page 6
3.2.6(e) Electron volt. (eV) This is the energy transferred when an electron moves
between two points with a potential difference of 1
volt between them. 1 eV = 1.6 × 10-19 J
3.2.6(f) Ionisation The removal of one or more electrons from an atom.
Ionisation energy The ionization energy of an atom is the minimum
energy needed to remove an electron from the atom.
Unit: J
3.2.6(i) Work function The work function of a surface is the minimum
energy needed to remove an electron from the
surface. Unit: J [or eV]
3.2.6(k) Photoelectric effect When light or ultraviolet radiation of short enough
wavelength falls on a surface, electrons are emitted
from the surface. This is the photoelectric effect.
Physics Terms Definitions and Units page 7
PH4
Ref Item Definition
Period T for a point
describing a circle.
3.4.1(a) Time taken for one complete circuit.
Frequency f. The number of circuits or cycles per second.
3.4.1(b) Angular velocity ω. For a point describing a circle at uniform speed, the
angular velocity ω is equal to the angle θ swept out
by the radius in time t divided by t . (ω= θ/t)
UNIT: [rad] s-1
Simple harmonic
motion (shm).
Shm occurs when an object moves such that its
acceleration is always directed toward a fixed point
and proportional to its distance from the fixed point.
(a=-ω
2
x)
3.4.1(d)
Simple harmonic
motion (shm).
(Alternative
definition).
If the displacement x of a point changes with time t
according to the equation x = a sin(ωt+ε) where a, ω
and ε are constants, the motion of that point is shm.
[Variations of this kind are said to be sinusoidal
because they are determined by a sine term.]
Period T for an
oscillating body
3.4.1(h) Time taken for one complete cycle.
Amplitude A of an
oscillating object
The maximum value of the objectís displacement
(from its equilibrium position).
Free oscillations. Free oscillations occur when an oscillatory system
(such as a mass on a spring, or a pendulum) is
displaced and released.
 [The frequency of the free oscillations is known as
the natural frequency.]
3.4.1(n)
Damping. Damping is the dying away of amplitude with time of
free oscillations due to resistive forces.
Forced oscillations. These occur when a sinusoidally varying force is
applied to an oscillatory system, causing the system
to oscillate with the frequency of the applied force.
3.4.1(p)
Resonance. If, in forced vibrations, the frequency of the applied
force is equal to the natural frequency of the system
(e.g. mass on spring), the amplitude of the resulting
oscillations is very large. This is resonance.

Momentum The momentum of an object is its mass multiplied by
its velocity. (p = mv). It is a vector.
UNIT: kg m s-1
3.4.2(a)
Newtonís Laws of
Motion. 1st Law
An object continues in a state of uniform motion in a
straight line, or remains at rest, unless acted upon by
a resultant force.
Physics Terms Definitions and Units page 8
Newtonís Laws of
Motion. 2nd Law
The rate of change of momentum of an object is
proportional to the resultant force acting on it, and
takes place in the direction of that force.
3.4.2(a)
Newtonís Laws of
Motion. 3rd Law
If an object A exerts a force on a second object B,
then B must exert a force which is equal in
magnitude but opposite in direction on A.
Elastic collision. A collision in which there is no loss of kinetic
energy.
3.4.2(c)
Inelastic collision. A collision in which kinetic energy is lost.

3.4.3(a) Work. Work done by a force is the product of the magnitude
of the force and the distance moved in the direction
of the force.( W.D. = Fxcosθ)
UNIT: joule (J) [= Nm]
3.4.3(c) Hookeís Law. The extension of an elastic object such as a wire or
spring is proportional to the stretching force,
provided the extension is not too large.
(F = kx).
Energy The energy of a body or system is the amount of
work it can do. UNIT: joule (J).
3.4.3(d)
Power This is the work done per second, or energy
converted or transferred per second.
UNIT: watt (W) [= Js-1].
Conservation of
energy (principle
of).
Energy cannot be created or destroyed, only
transformed from one form to another.
3.4.3(e)
Potential energy. This is energy possessed by virtue of position. (e.g.
Gravitational PE = mgh)
3.4.3(h) Efficiency % Efficiency = 100×(Useful energy obtained)/(Total
energy input).
Internal energy The internal energy (of say a container of gas) is the
sum of the potential and kinetic energies of the
molecules.
3.4.3(i)
Thermodynamics.
First Law
The heat supplied to a system (e.g. a mass of gas) is
equal to the increase in internal energy plus the work
done by the system. (Q = ∆U + W). [The law is
essentially a restatement of the law of conservation of
energy including heat as an energy form. Any of the
terms in the equation can be positive or negative, e.g.
if 100 J of heat is lost from a system Q =  100 J]
3.4.3(n) Specific heat
capacity c.
The heat required, per kilogram, per degree Celsius
or Kelvin, to raise the temperature of a substance.
UNIT: J kg-1 K-1 or J kg-1°C-1
Physics Terms Definitions and Units page 9
 Mole. This is the amount of substance that has the same
number of particles (usually atoms or molecules) as
there are atoms in exactly twelve grammes of the
nuclide C12 .

3.4.4(a) Avogdadro constant
NA.
This is the number of particles in a mole.
(NA=6.02×1023 to 3 figs).
Boyleís law For a fixed mass of gas at constant temperature, the
pressure varies inversely as the volume. (p = k/V)
3.4.4(c)
Ideal gas. An ideal gas strictly obeys the equation of state
pV = nRT.

3.4.5(a) Capacitor. A pair of parallel metal plates, a small distance apart,
insulated from one another.
3.4.5(c) Relative
permittivity εr.of an
insulator or
ëdielectricí
If capacitance is measured first with vacuum
between the plates and then with a slab of insulator
between, the capacitance increases by a factor εr

3.4.6(a) Root mean square
value (r.m.s.).
This is a form of average, which is really self
defined. Thus for three discrete quantities 1,2 and 3,
the r.m.s value is given by
( ) ( ) 1 2 3 3 2 16 2 2 2 + + / = . . For sinusoidal variations
the r.m.s. value over a complete cycle is given by the
peak (maximum) value divided by 2 .
(e.g. Irms =IO/ 2 )
3.4.6(e) Capacitor, reactance
of.
When an AC voltage is applied to a capacitor, the
reactance is given by XC = Vrms/Irms where Vrms and
Irms are, respectively, the voltage across and the
current ‘through’ the capacitor.
It is equal to 1/ωC (or 1/2πfC).
3.4.6(f) Inductor, reactance
of.
When an AC voltage is applied to an inductor, the
reactance is given by XL = Vrms/Irms where Vrms and
Irms are, respectively, the voltage across and the
current through the inductor.
It is equal to ωL (or 2πfL)
Physics Terms Definitions and Units page 10
PH5
3.5.1(c) Newtonís law of
gravitation.
The gravitational force between two objects is
directly proportional to the product of their masses
and inversely proportional to the distance between
their centres. F = Gm1m2/r2
Electric field
strength E.
The force experienced per unit charge by a small
positive charge placed in the field. Unit: Vm-1.
Gravitational field
strength g.
The force experienced per unit mass by a mass
placed in the field. Unit: ms-2 or Nkg-1.
Electric potential
VE.
Electric potential at a point is the work done per unit
charge in bringing a positive charge from infinity to
that point. Unit: V. [= JC-1]
3.5.1
Gravitational
potential Vg.
Gravitational potential at a point is the work done
per unit mass in bringing a mass from infinity to that
point. Unit: Jkg-1.

3.5.2(c) Magnetic flux
density B.
A length l of wire perpendicular to a magnetic flux
density B, carrying a current I, experiences a force of
magnitude BIl. Unit: T (Tesla) [= NA-1m-1]
3.5.2(i) Relative
permeability µr.
When magnetic material of relative permeability µr
fills a long solenoid, the magnetic flux density in the
material is given by B = µrB0 where B0 is the flux
density when the solenoid is evacuated.
3.5.2(l) Ampere A. The ampere is that constant current which when
flowing through two infinite, thin, parallel wires, one
metre apart in vacuum, produces a force between the
wires of 2×10-7N per metre of length. Unit: A.

3.5.3(a) Magnetic flux φ.
Weber Wb.
If a single-turn coil of wire encloses an area A, and a
magnetic field B makes an angle θ with the normal
to the plane of the coil, the magnetic flux through the
coil is given by Ф = AB cos θ. Unit: Wb=Tm2
.
3.5.3(a) Flux linkage NФ. If the above coil consists of N turns, the flux linkage
is given by NФ . Unit: Wb or Wb turn.
Faradayís law When the flux linking an electrical circuit is
changing, an emf is induced in the circuit of
magnitude equal to the rate of change of flux.
3.5.3(b)
Lenzís Law. The direction of any current resulting from an
induced emf is such as to oppose the change in flux
linkage that is causing the current.
3.5.3(e) Self inductance L.
Henry H
When a current I through a coil produces a flux
linkage NФ, the self inductance of the coil is given
by L= NФ/I.
Unit: H=WbA-1=Tm2
A-1 [= VsA-1]

Physics Terms Definitions and Units page 11
α radiation A stream of helium He 4
2 nuclei.
β radiation A stream of electrons.
γ radiation Short wavelength electromagnetic radiation (shorter
than X-rays).
3.5.4(a)
3.5.4(a)
3.5.4(a)
3.5.4(a) XA
Z notation X is the chemical symbol of the element, A the mass
number (number of protons plus number of neutrons)
and Z the atomic number (number of protons).
3.5.4(d) Half life 1
2
T The time taken for the number of radioactive nuclei
N (or the activity A) to reduce to one half of the
initial value. Unit: s.
3.5.4(e) Activity A.
Becquerel Bq.
The rate of decay (number of disintegrations per
second) of a sample of radioactive nuclei.
Unit: Bq=s-1.
3.5.4(f) Decay constant λ. The constant which appears in the exponential decay
law t N N e−λ = 0 and determines the rate of decay (the
greater λ is, the more rapid the rate of decay). It is
related to half life by λ = ln2/ 1
2
T .
Unit: s-1
3.5.4(i) Radioisotopes Isotopes (of the same element) have the same atomic
number Z but different mass number A.
Radioisotopes are simply isotopes which are
radioactive.

Unified atomic
mass unit u.
The unified atomic mass unit is defined as exactly
one twelfth of the mass of one atom of carbon 12.
Thus one atom of C12 has a mass of exactly 12u.
(1u = 10-3 / NA = 1.66x10-27kg)
Electron volt (eV). This is the energy transferred when an electron
moves between two points with a potential
difference of 1 volt between them. 1 eV = 1.6 ×
10-19 J
[Within the context of particle accelerators it can
also be defined as: the energy acquired by an
electron when accelerated through a pd of 1V.]
3.5.5(b)
Binding energy of a
nucleus.
The energy that has to be supplied in order to
dissociate a nucleus into its constituent nucleons. [It
is therefore not energy which a nucleus possesses.]
Unit: J [or MeV]
3.5.6(f) De Broglie
relationship λ = h/p
The key relationship relating to wave-particle
duality. It gives the wavelength λ associated with a
moving particle in terms of its linear momentum p
and the Planck constant h.