Unit 3 Specification

3.1 Circular Motion

(a) the terms period of rotation, frequency

(b) the definition of the unit radian as a measure of angle

(c) the use of the radian as a measure of angle

(d) the definition of angular velocity, ω, for an object performing circular motion and performing simple harmonic motion

(e) the idea that the centripetal force is the resultant force acting on a body moving at constant speed in a circle

(f) the centripetal force and acceleration are directed towards the centre of the circular motion

(g) the use of the following equations relating to circular motion

v = ωr , a = ω²r , a = v²/r , F = mv² / r , F mω²r

3.2 Vibrations

(a) the definition of simple harmonic motion as a statement in words

(b) a = −ω²x as a mathematical defining equation of simple harmonic motion

(c) the graphical representation of the variation of acceleration with displacement during simple harmonic motion

(d) x = Acos(ωt + ε) as a solution to a = −ω²x

(e) the terms frequency, period, amplitude and phase

(f) period as 1/f or 2𝛑 / ω

(g) v = Aωsin(ωt + ε) for the velocity during simple harmonic motion

(h) the graphical representation of the changes in displacement and velocity with time during simple harmonic motion

(i) the equation T = 2𝛑 √m/k for the period of a system having stiffness (force per unit extension) k and mass m

(j) the equation T = 2𝛑 √l/g for the period of a simple pendulum

(k) the graphical representation of the interchange between kinetic energy and potential energy during undamped simple harmonic motion, and perform simple calculations on energy changes

(l) free oscillations and the effect of damping in real systems

(m) practical examples of damped oscillations

(n) the importance of critical damping in appropriate cases such as vehicle suspensions

(o) forced oscillations and resonance, and to describe practical examples

(p) the variation of the amplitude of a forced oscillation with driving frequency and that increased damping broadens the resonance curve

(q) circumstances when resonance is useful for example, circuit tuning, microwave cooking and other circumstances in which it should be avoided for example, bridge design

3.3 Kinetic Theory

(a) the equation of state for an ideal gas expressed as pV nRT = where R is the molar gas constant and pV NkT = where k is the Boltzmann constant

(b) the assumptions of the kinetic theory of gases which includes the random distribution of energy among the molecules

(c) the idea that molecular movement causes the pressure exerted by a gas, and use p = 1/3 ρc² or 1/3 N/V mc² where N is the number of molecules

(d) the definition of Avogadro constant N_A and hence the mole

(e) the idea that the molar mass M is related to the relative molecular mass Mr by M / kg= M_r/1000 , and that the number of moles n is given by total mass molar mass

(f) how to combine pV = 1/3 Nmc² with pV = nRT and show that the total translational kinetic energy of a mole of a monatomic gas is given by 3/2 RT and the mean kinetic energy of a molecule is 3/2 kT where k = R/N_A is the Boltzmann constant, and that T is proportional to the mean kinetic energy

3.4 Thermal Physics

(a) the idea that the internal energy of a system is the sum of the potential and kinetic energies of its molecules

(b) absolute zero being the temperature of a system when it has minimum internal energy

(c) the internal energy of an ideal monatomic gas being wholly kinetic so it is given by U = 3/2 nRT

(d) the idea that heat enters or leaves a system through its boundary or container wall, according to whether the system's temperature is lower or higher than that of its surroundings, so heat is energy in transit and not contained within the system

(e) the idea that if no heat flows between systems in contact, then they are said to be in thermal equilibrium, and are at the same temperature

(f) the idea that energy can enter or leave a system by means of work, so work is also energy in transit (g) the equation W = pΔV can be used to calculate the work done by a gas under constant pressure

(h) the idea that even if p changes, W is given by the area under the p – V graph

(i) the use of the first law of thermodynamics, in the form ΔU= Q − W and know how to interpret negative values of ΔU, Q, and W

(j) the idea that for a solid (or liquid), W is usually negligible, so Q = ΔU

(k) Q =mcΔθ , for a solid or liquid, and this is the defining equation for specific heat capacity, c

3.5 Nuclear Decay

(a) the spontaneous nature of nuclear decay; the nature of α, β and γ radiation, and equations to represent the nuclear transformations using the 𝐴/𝑍 X notation

(b) different methods used to distinguish between α, β and γ radiation and the connections between the nature, penetration and range for ionising particles

(c) how to make allowance for background radiation in experimental measurements

(d) the concept of the half-life, T_½

(e) the definition of the activity, A, and the Becquerel

(f) the decay constant, λ, and the equation A = λ N

(g) the exponential law of decay in graphical and algebraic form,

N = N_o e^-λt and A = A_o e^-λt

or

N = N_o / 2^x and A = A_o / 2^x

where x is the number of half-lives elapsed – not necessarily an integer

(h) the derivation and use of λ = ln2 / T_½

3.6 Nuclear Energy

(a) the association between mass and energy and that E = mc²

(b) the binding energy for a nucleus and hence the binding energy per nucleon, making use, where necessary, of the unified atomic mass unit (u)

(c) how to calculate binding energy and binding energy per nucleon from given masses of nuclei

(d) the conservation of mass / energy to particle interactions – for example: fission, fusion

(e) the relevance of binding energy per nucleon to nuclear fission and fusion making reference when appropriate to the binding energy per nucleon versus nucleon number curve