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A Level Physics 9702 Paper 4 Summary
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CAIE AS Level Physics (9702) – Paper 4Motion in a Circle: • The gravitational force between two masses is independent of
• Radian: the angle subtended at the centre of the circle by an the medium separating the mass and is always an attractive
arc of length equal to the radius of the circle force.
• Angular displacement: the angle through which an object • A satellite in a geostationary orbit remains at the same point
moves through a circle above the Earth’s surface, with an orbital period of 24 hours,
arc length orbiting from west to east, directly above the Equator.
angle (in radians) =
radius
𝒔
𝜽= Gravitational Field Strength:
𝒓
• Angular velocity: the rate of change of the angular position of • How strong or weak a gravitational field is.
an object as it moves along a curved path • By equating W = mg and Newton’s Law of Gravitation:
angular displacement 𝐆𝒎𝟏 𝒎𝟐
Angular speed = 𝒎𝒈 =
time taken 𝒓𝟐
𝚫𝜽 𝐆𝑴
𝝎= ∴𝒈=
𝚫𝒕 𝒓𝟐
• Period: the time taken by the body to complete the circular
path once Gravitational Potential:
𝝎=
𝟐𝛑 • The work done per unit mass in bringing a mass from infinity
𝐓 to the point
• Relating angular velocity and linear velocity: 𝐆𝑴
o The speed of an object travelling around a circle depends ∅=−
𝐫
on its angular speed (ω) and its distance from the centre • The negative sign is because:
speed = angular speed x radius o Gravitational force is always attractive
𝒗 = 𝝎×𝒓 o Gravitational potential reduces to zero at infinity
o Gravitational potential decreases in direction of field
Circular Motion:
• A body moving in a circle at a constant speed changes velocity
since its direction changes. Thus, it is accelerating and hence
experiences a force.
• Centripetal force: resultant force acting on an object moving
in a circle, always directed towards the centre of the circle
perpendicular to the velocity of the object
𝒎𝒗𝟐 • Gravitational potential energy of a mass at a point in the
𝑭= = 𝒎𝒓𝝎𝟐
𝐫
gravitational field of another mass M, is the work done in
• Centripetal acceleration: derived by equating Newton’s 2nd
bringing that mass from infinity to that point
law and centripetal force
𝐆𝑴
𝒗𝟐 𝑬𝒑 = 𝒎∅ = − 𝒎
𝒂= 𝒐𝒓 𝒂 = 𝒓𝝎𝟐 𝐫
𝐫
• The gravitational potential energy difference between two
points is the work done in moving a mass from one point to
Gravitational Fields: another
• Gravitational field: an example of a field of force
∆𝑬𝒑 = 𝒎∅𝒇𝒊𝒏𝒂𝒍 − 𝒎∅𝒊𝒏𝒊𝒕𝒊𝒂𝒍
• Gravitational field strength: gravitational force per unit mass
Representing a Gravitational Field:
• Gravitational field lines how the direction and strength of the
Temperature:
gravitational force • Temperature does not measure the amount of thermal energy
• For an isolated point mass, the gravitational field is radial in in a body:
shape with the mass at the centre o Two objects of different masses made of the same
material at the same temperature would have different
• A higher density of field lines a region of stronger field
amount of heat
• The gravitational force gets weaker as you go further away.
o When a substance melts or boils, heat is input but there
is not temperature energy
Newton’s Law of Gravitation:
• The gravitational force between two-point masses is
Thermal Equilibrium:
proportional to the product of their masses & inversely
• Thermal energy is transferred from a region of higher
proportional to the square of their separation
𝐆𝒎𝟏 𝒎𝟐 temperature to a region of lower temperature
𝑭= • Thermal equilibrium: Regions of equal temperature are in
𝒓𝟐
thermal equilibrium. When two or more objects in contact
have the same temperature so there is no net flow of energy
between them.
1
, CAIE AS Level Physics (9702) – Paper 4
Measuring Temperature: Determining Specific Heat Capacity, c
• A physical property that varies with temperature may be used • Quantities required:
for the measurement of temperature • Mass at time intervals Voltage and current supplied
o Change in volume of a liquid or gas
o Change in pressure of a gas
o Change in electrical resistance
o Change in e.m.f. of a thermocouple.
• The scale of thermodynamic temperature does not depend on
the property of any particular substance
• Absolute zero: the lowest possible temperature on the
thermodynamic temperature scale is 0 Kelvin.
o Impossible to remove any more energy
𝑲 = °𝑪 + 𝟐𝟕𝟑. 𝟏𝟓
Specific Heat Capacity and Latent Heat:
• Specific heat capacity: energy required per unit mass of the
• Beaker containing water heated to 100 oC and maintained
substance to raise the temperature by 1 Kelvin
𝐄 • Mass readings taken at regular time intervals
𝒄= • Plot graph of mass against time
𝒎∆𝜽
Determining Specific Heat Capacity, c Ideal Gases:
• Quantities required: • Avogadro’s constant (NA): number of atoms present in 12g of
o Accurate measurement of mass carbon-12
o Temperature at time intervals
• A mole: amount of substance containing same number of
o Voltage and current supplied particles as in 12g of carbon-12
Equations of State:
• Ideal gas: a gas which obeys 𝒑𝑽 ∝ 𝑻, where T is the
thermodynamic temperature
𝒑𝑽 = 𝒏𝑹𝑻
(n = amount of substance [no. of moles])
𝒑𝑽 = 𝑵𝒌𝑻
(N = number of molecules)
Boltzmann’s constant:
𝑹
• Measure temperature at regular time intervals and plot graph 𝒌=
𝑵𝑨
of temperature against time
• Divide quantity of heat equation with time Kinetic Theory of Gases:
𝑬 ∆𝜽
=( ) • Gas contains large no. of particles colliding with the walls of
∆𝒕 ∆𝒕 the container and with each other.
𝑬
• is the power supplied 𝑷 and 𝑷 = 𝑽𝑰 o Kinetic energy cannot be lost
∆𝒕
∆𝜽
• is the gradient of the graph plotted • Negligible intermolecular forces of attraction, except during
∆𝒕
𝑽𝑰 = 𝒎𝒄 × 𝒈𝒓𝒂𝒅𝒊𝒆𝒏𝒕 collision
• Volume of particles negligible compared to volume of
• Specific latent heat of fusion: energy required per unit mass of container
a substance to change from solid to liquid phase without any o The particles are much further apart
change in temperature • Collisions between particles are perfectly elastic
• Specific latent heat of vaporization: energy required per unit • The time of collision by a particle with the container walls is
mass of a substance to change from liquid to gas negligible compared with the time between collisions.
𝑬 = 𝒎𝑳 o Molecules are hard spheres
• Specific latent heat of vaporization is always greater than that • Average k.e. directly proportional to absolute temperature.
of fusion for a given substance because:
o During vaporization, there is a greater increase in volume Molecular Movement and Pressure:
than in fusion; thus more work done against atmosphere • Pressure of an ideal gas:
o In vaporization, particles need to be separated further 𝟏
𝒑𝑽 = 𝑵𝒎 < 𝒄𝟐 >
apart than in fusion, so more work is done against forces 𝟑
of attraction when vaporizing • The average value of 𝒄𝟐 is < 𝒄𝟐 > (mean square velocity)
• Root mean square speed cr.m.s. is given by is √< 𝒄𝟐 >
2
, CAIE AS Level Physics (9702) – Paper 4
Kinetic Energy of a Molecule: Acceleration:
• By equating the two formulae in pV, finding a relationship 𝒂 = −𝝎𝟐 𝒙
between Ek and T The minus sign shows that, when the object is displaced to the
right, the direction of its acceleration is to the left.
𝒂 = −𝝎𝟐 (𝒙𝟎 𝐬𝐢𝐧 (𝝎𝒕)) 𝒂 = −𝝎𝟐 (𝒙𝟎 𝐜𝐨𝐬 (𝝎𝒕))
Internal Energy:
• Internal energy: sum of random distribution of kinetic and
potential energies of molecules in a system
• Internal energy is determined by the state of the system
Internal Energy = Total P.E. + Total K.E. Energy in SHM:
• A rise in temperature of an object is an increase in its internal
energy
First Law of Thermodynamics:
• First law of thermodynamics: 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
∆𝑼 = 𝒒 + 𝑾
• ∆𝑼 : Increase in internal energy of the system
• 𝒒 : heat supplied to the system
• 𝑾 : work done on the system
Oscillations:
• Displacement (x): instantaneous distance of the moving object
from its mean position
• Amplitude (A): maximum displacement from the mean
position
• Period (T): time taken for one complete oscillation
• Frequency (f): number of oscillations per unit time
• Angular frequency (𝝎): rate of change of angular
displacement
𝝎 = 𝟐𝝅𝒇
• Phase difference (𝝓): measure of how much one wave is out
of step with another wave
Simple Harmonic Motion:
• Simple harmonic motion: acceleration is proportional to
displacement from a fixed point and in the opposite direction
𝒂 = −𝝎𝟐 𝒙
Displacement:
𝒙 = 𝒙𝟎 𝒔𝒊𝒏(𝝎𝒕) 𝒙 = 𝒙𝟎 𝒄𝒐𝒔(𝝎𝒕)
Velocity:
𝒗 = ±𝝎 √(𝒙𝟐𝟎 − 𝒙𝟐 )
𝒗 = −𝒗𝟎 𝒔𝒊𝒏(𝝎𝒕) 𝒗 = 𝒗𝟎 𝒄𝒐𝒔(𝝎𝒕)
3
, CAIE AS Level Physics (9702) – Paper 4
Damping: Coulomb’s Law:
• Damping: loss of energy and reduction in amplitude from an • Coulomb’s Law states: Any two-point charges exert an
oscillating system caused by force acting in opposite direction electrical force on each other that is proportional to the
to the motion (e.g. friction) product of their charges and inversely proportional to the
• Light damping: system oscillates about equilibrium position square of the distance between them
𝑸𝟏 𝑸𝟐
with decreasing amplitude over a period of time 𝑭=
𝟒𝝅𝜺𝟎 𝒓𝟐
Electric Potential:
• Electric potential at a point is the work done in brining unit
positive charge from infinity to that point.
𝑸
𝑽=
𝟒𝝅𝜺𝟎 𝒓
• Critical damping: system does not oscillate & is amount of • Electric fields at a point is equal to the negative of potential
damping required such that the system returns to its gradient as that point.
equilibrium position in the shortest possible time • Electric potential energy between two points is the work done
• Heavy damping: damping is so great that the displaced object in a moving positive charge from one point to the other.
𝑸𝒒
never oscillates but returns to its equilibrium position very 𝑬𝒑 =
𝟒𝝅𝜺𝟎 𝒓
slowly
Capacitance:
• Capacitance: the ratio of charge stored by a capacitor to the
potential difference across it
• Farad (F): Unit of capacitance, 1 coulomb per volt.
𝑸
• Natural frequency: the unforced frequency of oscillation of a 𝑪=
𝑽
freely oscillating object • The capacitance of a capacitor is directly proportional to the
• Free oscillation: oscillatory motion not subjected to an area of the plates and inversely proportional to the distance
external periodic driving force; oscillates at natural freq. between the plates
• Forced oscillation: oscillation caused by an external driving
force; frequency is determined by driving force Capacitors:
• Resonance: the maximum amplitude of vibration when • Function: storing energy
impressed frequency equals natural frequency of vibration • Usage: Time delay, power smoothing and protection against
surges and spikes
• Dielectric: an electrical insulator
Electric Fields: How a Capacitor Stores Energy:
• Electric field: a field of force that can be represented by field • On a capacitor, there is a separation of charge with positive on
lines. one plate and negative on the other.
• To separate the charges, work must be done hence energy is
released when charges come together
• Direction of field lines show the direction of the field – always
from the positive charge to the negative
• Higher density of lines shows a stronger region of field
• Electric field strength at a point is the force per unit positive
charge that acts on a stationary charge Capacitors in Parallel:
𝐟𝐨𝐫𝐜𝐞
𝐟𝐢𝐞𝐥𝐝 𝐬𝐭𝐫𝐞𝐧𝐠𝐭𝐡 =
𝐜𝐡𝐚𝐫𝐠𝐞
𝑭
𝑬=
𝑸
• There is a uniform field between charged parallel plates
𝐩𝐨𝐭𝐞𝐧𝐭𝐢𝐚𝐥 𝐝𝐢𝐟𝐟𝐞𝐫𝐞𝐧𝐜𝐞
𝐟𝐢𝐞𝐥𝐝 𝐬𝐭𝐫𝐞𝐧𝐠𝐭𝐡 =
𝐬𝐞𝐩𝐞𝐫𝐚𝐭𝐢𝐨𝐧
𝑽 𝑪𝑻𝒐𝒕𝒂𝒍 = 𝑪𝟏 + 𝑪𝟐 + 𝑪𝟑
𝑬=
𝒅
Electric Field Strength:
𝑸
𝑬=
𝟒𝝅𝜺𝟎 𝒓𝟐
4
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