Physics Summary(Definitions and Equations)
Measurement
1. Physical quantity​ is a term used to measure a physical phenomenon
quantitatively.
2. Base unit​ is independent of other units for its definition.
3. Derived unit​ is a unit expressed in terms of the product or quotient of base
units.
4. Error​ is the difference between a measured value of a physical quantity and
its true value.
5. Random errors​ are errors of measurements in which the measured
quantities deviate from the mean value with varying magnitudes and different
signs.
6. Systematic errors​ are errors of measurements in which the measured
quantities deviate from the true value by a fixed magnitude and constant sign.
7. Accuracy​ is a measure of how close the measured value is to the true value.
8. Precision​ is a measure of how close each measured value agrees with one
another.
9. Uncertainty​ is the quantification of the doubt about the measurement value.
10. Actual uncertainty​ is the uncertainty of a measurement due to limitation of
the instrument.
11. Scalar quantity​ are quantity that has only magnitude.
12. Vector quantity​ are quantity with both magnitude and direction.
Useful equations
If A=B±C, then ΔA=ΔB+ΔC
If X=YZ or Y/Z, then ΔX/X=ΔY/Y+ΔZ/Z
If X= Y​3​ x Z​2​ , then ΔX/X=3ΔY/Y+2ΔZ/Z
ΔW=½ (maximum W-minimum W)
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Kinematics
1. Distance​ is the total length of the actual path travelled.
2. Displacement​ is the length and definition of the straight line drawn from the
starting position to the final position of the particle.
3. Speed​ is the rate of change of distance travelled with respect to time.
4. Average speed​ is the total distance travelled over the total time of travel.
5. Velocity​ is the rate of change of displacement with respect to time.
6. Acceleration​ is the rate of change of velocity with respect to time.
Useful equations
v=u+at
s=ut+1/2at​2
v​2​=u​2​+2as
2
Dynamics
1.
2.
3.
4.
5.
Force​ is rate of change of momentum.
Mass​ is a measure of the quantity of matter in a body.
Inertia ​is the natural resistance to change of velocity.
Weight ​is the attractive force exerted on an object by the Earth.
Contact forces​ are forces acting between two objects which are in physical
contact.
6. Non-contact forces​ are forces acting between objects which are not in
physical contact.
7. Linear momentum ​of a body is the product of its mass and velocity.
8. Impulse​ of a body is the product of a force and time of impact.
9. Principle of conservation of momentum​ states that the total momentum in
a closed system remains constant if the resultant force acting on the system is
zero.
10. Newton’s first law of motion​ states that a body will remain at rest or
continue to move with a constant velocity unless acted upon by a net external
force.
11. Newton’s second law of motion​ states the rate of change of a momentum of
a body is directly proportional to the resultant force acting on the body and in
the direction of the resultant force.
12. Newton’s third law of motion​ states that the forces of action and reaction
between interacting bodies are equal in magnitude, but opposite in direction,
are of the same type and act on different bodies.
Useful equations
p=mv
W=mg
F=ma
Δp=F x Δt
m​1​u​1​+m​2​u​2​=m​1​v​1​+m​2​v​2
u​1​-u​2​=v​2​-v​1
Average force= (final momentum-initial momentum)/time
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Forces
1. Frictional force​ is the force exerted by the surface on the object as an object
moves across it.
2. Static friction​ is a force at interface between two stationary surface, which
prevents them from sliding over one another.
3. Kinetic friction​ is a force at interface between two surfaces moving relative
to each other, which opposes the sliding motion.
4. Pressure​ is defined as force per unit area.
5. Upthrust ​is the net force acting on an object in the vertically upwards
direction as a result of the object being partially or totally immersed in a fluid.
6. Archimedes’ Principle​ states that an object immersed in a fluid, totally or
partially, experiences an upthrust, which is equal to the weight of fluid
displaced.
7. Principle of floatation​ states that for object floating equilibrium, the upthrust
is equal to weight of object.
8. Hooke’s Law​ states that stress is proportional to strain, provided that the
elastic limit is not exceeded.
9. Centre of gravity​ of an object is the point through which the entire weight the
body acts.
10. Moment of a force​ about a point is the turning effect of the force about that
point and is equal to the product of that force and the perpendicular distance
from its line of action to the point.
11. A​ couple​ is defined as a pair of equal but oppositely directed parallel forces,
whose line of action do not coincide.
12. Principle of moments ​states that for a body to be in rotational equilibrium,
the sum of clockwise moments about a pivot must be equal to the sum of
anticlockwise moments about the same pivot.
Useful equations
P=F/A
Pressure of static fluid= ​p​gh
F=kx
EPE of a spring=1/2kx​2
Moment of a force= F x d
4
Work,Energy and Power
1. The​ work done​ by a force on a body is the product of the force and the
displacement of body in direction of a force.
2. 1 Joule​ is the work done by a force of 1 Newton when its point of application
moves through a displacement of 1 metre in the direction of the force.
3. Kinetic energy​ is a type of energy which a body possess by virtue of its
motion.
4. Potential energy​ is the energy possessed by a mass by virtue of its position
and shape.
5. Gravitational potential energy​ is energy possessed by a mass by virtue of
its position in a gravitational field.
6. Mechanical energy​ of a system is defined as the sum of kinetic energy and
potential energy of the system.
7. Principle of conservation of energy​ states that total energy of an isolated
system is constant.
8. Power​ is the rate of work done.
Useful equations:
F=F x s(cosθ)
KE=½ mv​2
GPE=mgh
KE​initial​+PE​initial​+E​supplied​=KE​final​+PE​final​+E​lost
P=Fv
Efficiency=(useful energy input/energy input) x 100%
5
Circular motion
1. A ​radian​ is the angle subtended by an arc where the arc length is equal to the
radius.
2. Angular displacement​ is the angle an object turns about a fixed point.
3. Angular velocity​ of an object is defined as the rate of change of angular
displacement.
4. Period​ is the time to make one revolution.
5. Frequency​ is the number of revolutions the object makes per unit time.
6. Centripetal force​ is the net force acting on an object moving in a uniform
circular motion.
Useful equations:
T=2𝜋/ω
f=ω/2𝜋
F=ma​c​=mv​2​/r=mrω​2
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Gravitational Field
1. Newton’s law of Gravitation​ states that the mutual force of attraction
between any two point masses is directly proportional to the product of their
masses and inversely proportional to the square of separation between their
centres.
2. Gravitational field​ is a region of space in which any object lies in it
experiences a gravitational force towards the object that creates the field,due
to its mass.
3. Gravitational field strength​ is the gravitational force per unit mass acting on
a small test mass placed at that point.
4. Gravitational potential energy​ of an object is the work done in bringing the
point mass from infinity to that point.
5. Gravitational potential​ is the work done per unit mass in bringing a small
test mass from infinity to that point.
6. Equipotential lines​ are lines that trace positions of equal potential
7. A​ geostationary satellite​ rotates around the Earth such that it is always
positioned above the same point on the Earth’s surface.
8. Kepler’s Third Law ​states that the square of the period of an object in
circular orbit is directly proportional to the cube of the radius of its orbit.
Useful equations:
F=GMm/r​2
g=GM/r​2
U=-GMm/r
ɸ=-GM/r
F=-dU/dr
g=-dɸ/dr
T​2​ ∝ r​3
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Oscillation
1. Amplitude​ is the magnitude of the maximum displacement from the
equilibrium position.
2. Angular frequency​ is the circular representation of frequency.
3. Simple harmonic motion​ is a motion where the acceleration of an object is
always directed towards a fixed point, and proportional to its displacement
from that fixed point.
4. Damping ​refers to the process whereby energy is lost from an oscillating
system due to resistive forces.
5. Resonance​ is the phenomenon when the driving frequency is close to or
equal to the natural frequency of the oscillating system, maximum energy is
transferred from the periodic force to the oscillating system which will vibrate
with maximum amplitude.
Useful equations:
v​o​=x​o​ω
a​o​=x​o​ω​2
v= ± ω√(x​o​2​-x​2​)
a=-ω​2​x
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Waves
1. Displacement​ is the distance of particle from equilibrium position with its
associated direction.
2. Amplitude​ is the magnitude of the maximum displacement from the
equilibrium position.
3. Period​ is the time taken for 1 complete cycle.
4. Frequency​ is the number of cycles per unit time made by a particle in the
wave.
5. Wavelength​ is the distance between 2 consecutive particles of the same
phase.
6. Speed​ is the distance moved by wavefront per unit time.
7. Transverse waves​ are where displacement of particles is perpendicular to
the direction of wave propagation.
8. Longitudinal waves​ are where displacement of particles occurs along the
direction of propagation.
9. Phase difference ​between two waves of the same frequency can be thought
of as a delay or advance in the start of one wave cycle with respect to
another.
10. Progressive​ refers to the phenomenon of energy being dispersed to the
space surrounding the source.
11. Intensity​ of a wave is the rate of transfer of energy from the same source per
unit area perpendicular to the direction of wave propagation.
12. Polarisation​ is a process by which a wave oscillations are made to occur in
one plane only.
Useful equations:
v=fλ
ɸ/2π=Δd/λ
ɸ/2π=Δt/T
P=IS
E∝A​2
I∝A​2
I=I​o​cos​2​θ
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Superposition
1. Principle of superposition​ states that when two or more waves of the same
type meet at a point in space, the resultant wave displacement at any point is
given by the vector sum of the individual wave displacements at that point.
2. Diffraction​ is the spreading or bending of waves through an aperture or
around an obstacle.
3. Coherent​ sources are sources with constant phase difference between them.
4. Resolving power​ of an optical instrument is its ability to distinguish between
any two clearly spaced objects.
Useful equations:
Path difference (Constructive interference)=nλ
Path difference (Destructive interference)=(n+½)λ
λ=ax/D
dsinθ=nλ
sinθ=λ/b
sinθ=1.22λ/b
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Temperature and Ideal Gas
1. Temperature​ is the measure of the degree of hotness.
2. Heat ​is the thermal energy transferred between a system and its environment
due to temperature difference.
3. Two systems in thermal contact are said to be in​ thermal equilibrium​ if there
is no net exchange in thermal energy between them.
4. Internal energy​ is the sum of the random distribution of kinetic and potential
energies associated with the molecules of a system.
5. An​ ideal gas​ is one in which the separation between the gas molecules is
sufficiently large such that the intermolecular forces between the gas
molecules are negligible.
6. 1 K​ is defined as 1/273.16 of the temperature of the triple point of water.
7. Triple point of water​ is that unique temperature at which pure ice, pure water
and pure water vapour co-exist in equilibrium.
8. Absolute zero​ is the temperature where all molecular motion is a minimum.
9. Ice point​ is the temperature at which pure ice can exist in equilibrium with
water at standard atmospheric pressure.
10. Steam point​ is the temperature at which water can exist in equilibrium with
vapour at standard atmospheric pressure.
11. One mole​ is the amount of substance that contains as many particles as
there are atoms in 12.0 g of carbon-12.
12. The ​Avogadro’s constant​ is the number of atoms in 0.0120kg of carbon-12.
13. Assumptions of Kinetic Theory of Gas:
● A gas consists of a very large number of molecules.
● The molecules are in constant random motion and obey Newton’s laws of
motion.
● Collision between gas molecules are elastic.
● Collision between gas molecules and walls of container are elastic.
● Intermolecular forces act only during collision between molecules. The
duration of a collision is negligible compared with the time interval between
collisions.
● The volume of the gas themselves is negligible compared with the volume
occupied by gas.
● Between collisions, a molecule moves with uniform velocity.
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Useful equations:
θ=(X​θ​-X​0​)/(X​100​-X​0​) x 100%
T/℃=T/K-273.15
pV=nRT
pV=NkT
½ m<c>​2​=3/2kT
U​ideal gas​=3/2NkT=3/2nRT=3/2pV
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First Law of Thermodynamics
1. Heat capacity​ of a body is the amount of heat that must be supplied to it to
cause a unit rise in temperature without a change in state.
2. Specific heat capacity​ of a body is the amount of heat that must be supplied
to it to cause a unit mass of the substance to undergo a unit rise in
temperature without a change in state.
3. Specific latent heat of fusion​ of a body is the amount of heat that must be
supplied to cause a unit mass of the body to undergo a phase change from
solid to liquid.
4. Specific latent heat of vaporisation ​of a body is the amount of heat that
must be supplied to cause a unit mass of the body to undergo a phase
change from liquid to vapour.
5. Melting​ is the process in which a substance changes its state from solid to
liquid at a constant temperature.
6. Boiling​ is the process in which a substance changes its state from liquid to
vapour at a constant temperature.
7. Evaporation​ is a cooling process by which a liquid becomes a vapour. It
occurs at all temperatures.
8. The ​First Law of Thermodynamics​ state that the increase in internal energy
of a system is equal to the sum of heat supplied to the system and the work
done on the system.
Useful equations:
Q=mcΔθ
l​f =Q/m
​
l​v​=Q/m
ΔU=Q​in​+W​on
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Electric Field
1. Coulomb’s Law of Electrostatics ​states that the magnitude of the force
between two point charges is directly proportional to the product of the
magnitude of the charges and inversely proportional to the square of their
separation.
2. Electric field​ produced by a charge is a region of space within in which an
electric force is experienced by another charge.
3. Electric field strength​ at a point is defined as the electric force exerted per
unit charge placed at that point.
4. Electric potential energy​ of a charge at a point is the work done in bringing
the charge from infinity to that point.
5. Electric potential​ at a point is the work done per unit positive charge in
bringing a point test charge from infinity to that point.
Useful equations:
F​E​=(1/4πε)(Qq/r​2​)
E=(1/4πε)(Q/r​2​)
E=F/q
U​E​=Qq/4πεr
V=Q/4πεr
E=-dV/dr
E=ΔV/d
F​E​=qE
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Current of Electricity
1. Electric current​ is the rate of flow of charged particles.
2. Charge​ is a physical property of matter that causes it to experience a force
when it is in electric field.
3. One Coulomb​ is the amount of charge which passes through a given
cross-section of a wire in 1 second when a constant current of 1 ampere is
flowing.
4. Current​ is the rate of flow of electric charge.
5. Resistance​ is the ratio of potential difference across to the current I flowing
through it.
6. Power​ is the rate of work done.
7. Electromotive force​ of a source is the amount of energy converted from
other forms of energy into electrical energy when a unit charge is driven
through the source round a complete circuit.
8. Potential difference​ between 2 points in a circuit is the energy converted
from other forms of energy when an unit charge passing from one point to the
other.
Useful equations:
Q=It
I=dQ/dt
I=nAqv
R=V/I
P=W/t=IV=I​2​R=V​2​/R
E=Ir+IR
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DC circuits
1. Thermistor​ is a resistor whose resistance decreases as temperature
increases.
2. Light dependent resistor ​is a resistor whose resistance decreases as light
intensity increases.
3. Potentiometer​ is a circuit arrangement which can be used to measure or
compare potential differences of emf of cells.
Useful equations:
R​eff​=R​1​+R​2
R​eff​=1/R​1​ +1/R​2
V​out​=R​1​/R​1​+R​2​ x V​in
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Electromagnetism
1. A​ magnetic field​ is a region in space where a magnetic force is experienced.
2. Magnetic flux density​ of a magnetic field is the force exerted on a unit length
of conductor carrying a unit current placed at right angles to the field.
3. One tesla​ is the magnetic flux density of a field in which a force of 1 N is
exerted on a conductor of length 1 metre carrying a current of 1 ampere
placed at right angles to the field.
Useful equations:
B=μ​o​I/2𝜋d
B=μ​o​NI/2r
B=μ​o​NI
F=BILsinθ
F=Bqvsinθ
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Electromagnetic Induction
1. Magnetic flux​ is the product of the magnetic flux density normal to the plane
of the surface and the area of the surface.
2. One weber​ is the magnetic flux passing through an area of 1 square metre
when the magnetic flux density normal to the area is 1 tesla.
3. Magnetic flux linkage​ is the product of magnetic flux passing through the coil
and the number of turns on the coil.
4. Faraday’s Law​ states that the magnitude of the induced emf is directly
proportional to the rate of change of magnetic flux linkage or the rate of
cutting of magnetic flux.
5. Lenz’s Law​ states that the direction of induced emf is such that the current
which causes it to flow opposes the change in magnetic flux which is
producing it.
Useful equations:
ɸ=BAcosθ
Φ=Nɸ=NBAcosθ
ε=-dΦ/dt=-d(Nɸ)/dt=-d(NBAcosθ)/dt
ε=Blv
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Alternating current
1. An ​alternating current​ is the flow of electric charges that periodically
reverses in direction.
2. An ​alternating voltage​ is a emf or pd that periodically reverses in direction.
3. R.m.s current​ is the effective direct current that produces the same heating
effect as the alternating current.
4. A ​transformer​ is used to change an alternating emf from one value to
another higher value or a lower value.
5. Rectification ​is the conversion of ac to dc using rectifiers.
6. Rectifier​ is a non-ohmic device whose resistance depends on the polarity of
the applied pd.
Useful equations:
I​rms​=I​o​/2
V​rms​=V​o​/2
P​ave​=(I​rms​)​2​R=(V​rms​)​2​/R
V​s​/V​p​=I​p​/I​s​=N​s​/N​p
V​p​I​p​=V​s​I​s​+ power loss
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Quantum Physics
1. The ​photoelectric effect​ is the emission of electrons from the surface of a
metal when electromagnetic radiation of high enough frequency is incident on
it.
2. A ​photon​ is a packet or a quantum of radiation energy.
3. Stopping potential​ is the minimum potential difference across the plates to
stop the fastest photoelectrons from reaching the collector.
4. Work function energy​ is the minimum energy required for an electron to
escape the metal surface.
5. Threshold frequency​ is the minimum frequency of incident radiation at which
photoelectrons are emitted from the surface of the metal.
6. 1 eV​ is the kinetic energy gained by an electron in being accelerated by a pd
of 1 V.
7. Ionization energy​ is the minimum energy required to remove the outermost
electron of an atom.
8. X rays​ are short wavelength electromagnetic radiation which are highly
energetic with wavelength of about 10​-11​ m.
Useful equations:
E=hf=hc/λ
E=ɸ+½ mv​max​2
ɸ=hf​o
½ mv​max​2​=eV​s
Intensity=n(hf)/time x area
λ​db​=h/mv
ΔxΔp≥h
ΔEΔt≥h
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Nuclear Physics
1. 𝞪-particle​ is the nucleus of a helium atom and is composed of 2 neutrons and
2 protons.
2. Nucleon number ​of an element is the number of nucleons in the nucleus of
an atom of the element.
3. Proton number ​of an element is the number of protons in the nucleus of an
atom of the element.
4. Isotopes​ are atoms of the same element with same number of protons but
different number of electrons.
5. The ​unified atomic mass​ is defined as equivalent to one-twelfth the mass of
a carbon-12 atom.
6. Binding energy​ is the energy given off by protons and neutrons to form
nucleus.
7. Binding energy per nucleon​ is the average energy that needs to be supplied
to remove a nucleon from the nucleus.
8. Nuclear fission​ is the disintegration of a heavy nucleus into two or more
lighter nuclei due to electron bombardment.
9. Nuclear fusion​ is the process of combining two light nuclei to produce a
heavier nucleus.
10. Count rate​ is a measure of the rate of radiation received by a radioactivity
detector.
11. Activity​ is defined as the rate of disintegration of the radioactive nuclei with
respect to time.
12. The ​decay constant​ is the probability that a nucleus will decay per unit time.
13. The ​half-life​ of a radioactive nuclide is the average time taken for half the
number of undecayed nuclei present in the source to disintegrate.
14. Background radiation​ is the radiation detected by a radiation counter when
the radioactive source is nearby.
Useful equations:
Mass defect=total mass of constituent protons and neutrons-mass of nucleus
Mass defect=total mass of constituent protons and neutrons and electrons-mass of
atom
E=mc​2
Binding energy per nucleon=B.E./A
Energy released=(total BE of products-total BE of reactants)
x=x​o​e​-λt​ where x can be N, A or C
t​1/2​=ln2/λ
x/x​o​=(½)​n
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