A-level Physics₇₄₀₈

Motion in a circular path at constant speed implies there is an acceleration and requires a centripetal force.

Magnitude of angular speed $\mathit{\omega }\mathsf{=}\frac{\mathit{v}}{\mathit{r}}\mathsf{=}\mathsf{2}\mathit{\pi }\mathit{f}$

Radian measure of angle.

Direction of angular velocity will not be considered.

Centripetal acceleration $\mathit{a}\mathsf{=}\frac{{\mathit{v}}^{\mathsf{2}}}{\mathit{r}}\mathsf{=}{\mathit{\omega }}^{\mathsf{2}}\mathit{r}$

The derivation of the centripetal acceleration formula will not be examined.

Centripetal force $\mathit{}\mathit{F}\mathsf{=}\frac{{\mathit{mv}}^{\mathsf{2}}}{\mathit{r}}\mathsf{=}\mathit{m}{\mathit{\omega }}^{\mathsf{2}}\mathit{r}$

MS 0.4

Estimate the acceleration and centripetal force in situations that involve rotation.

Analysis of characteristics of simple harmonic motion (SHM).

Condition for SHM: $\mathit{a}\mathsf{\propto }\mathsf{-}\mathit{x}$

Defining equation: $\mathit{a}\mathsf{=}\mathsf{-}{\mathit{\omega }}^{\mathsf{2}}\mathit{x}$

$\mathit{x}\mathsf{=}\mathit{A}\mathit{cos}\mathsf{}\mathit{\omega t}$ and $\mathit{v}\mathsf{=}\mathsf{\pm }\mathit{\omega }\sqrt{\left({\mathit{A}}^{\mathsf{2}}\mathsf{-}{\mathit{x}}^{\mathsf{2}}\right)}$

Graphical representations linking the variations of $\mathit{x}$ , $\mathit{v}$ and $\mathit{a}$ with time.

Appreciation that the $\mathit{v}\mathsf{-}\mathit{t}\mathit{ }$ graph is derived from the gradient of the $\mathit{x}\mathsf{-}\mathit{t}$ graph and that the $\mathit{a}\mathsf{-}\mathit{t}\mathit{ }$ graph is derived from the gradient of the $\mathit{v}\mathsf{-}\mathit{t}$ graph.

Maximum speed $\mathsf{=}\mathit{\omega A}$

Maximum acceleration $\mathsf{=}{\mathit{\omega }}^{\mathsf{2}}\mathit{A}$

AT i, k

Data loggers can be used to produce $\mathit{s}\mathsf{-}\mathit{t}$ , $\mathit{v}\mathsf{-}\mathit{t}$ and $\mathit{a}\mathsf{-}\mathit{t}\mathit{ }$ graphs for SHM.

MS 3.6, 3.8, 3.9, 3.12

Sketch relationships between $\mathit{x}$ , $\mathit{v}$ , $\mathit{a}$ and $\mathit{t}$ for simple harmonic oscillators.

Study of mass-spring system: $\mathit{T}\mathsf{=}\mathsf{2}\mathit{\pi }\sqrt{\frac{\mathit{m}}{\mathit{k}}}$

Study of simple pendulum: $\mathit{T}\mathsf{=}\mathsf{2}\mathit{\pi }\sqrt{\frac{\mathit{l}}{\mathit{g}}}$

Questions may involve other harmonic oscillators (eg liquid in U-tube) but full information will be provided in questions where necessary.

Variation of ${\mathit{E}}_{\mathrm{k}}$ , ${\mathit{ }\mathit{E}}_{\mathrm{p}}$ , and total energy with both displacement and time.

Effects of damping on oscillations.

MS 4.6 / AT b, c

Students should recognise the use of the small-angle approximation in the derivation of the time period for examples of approximate SHM.

Required practical 7: Investigation into simple harmonic motion using a mass–spring system and a simple pendulum.

Qualitative treatment of free and forced vibrations.

Resonance and the effects of damping on the sharpness of resonance.

Examples of these effects in mechanical systems and situations involving stationary waves.

AT g, i, k

Investigation of the factors that determine the resonant frequency of a driven system.

Internal energy is the sum of the randomly distributed kinetic energies and potential energies of the particles in a body.

The internal energy of a system is increased when energy is transferred to it by heating or when work is done on it (and vice versa), eg a qualitative treatment of the first law of thermodynamics.

Appreciation that during a change of state the potential energies of the particle ensemble are changing but not the kinetic energies. Calculations involving transfer of energy.

For a change of temperature: $\mathit{Q}\mathsf{=}\mathit{m}\mathit{c}\mathsf{∆}\mathit{\theta }$ where $\mathit{c}$ is specific heat capacity.

Calculations including continuous flow.

For a change of state $\mathit{Q}\mathsf{=}\mathit{m}\mathit{l}$ where $\mathit{l}$ is the specific latent heat.

MS 1.5 / PS 2.3 / AT a, b, d, f

Investigate the factors that affect the change in temperature of a substance using an electrical method or the method of mixtures.

Students should be able to identify random and systematic errors in the experiment and suggest ways to remove them.

PS 1.1, 4.1 / AT k

Investigate, with a data logger and temperature sensor, the change in temperature with time of a substance undergoing a phase change when energy is supplied at a constant rate.

Gas laws as experimental relationships between $\mathit{p}$ , $\mathit{V}$ , $\mathit{T}$ and the mass of the gas.

Concept of absolute zero of temperature.

Ideal gas equation: $\mathit{p}\mathit{V}\mathsf{=}\mathit{n}\mathit{R}\mathit{T}$ for $\mathit{n}$ moles and $\mathit{p}\mathit{V}\mathsf{=}\mathit{N}\mathit{k}\mathit{T}$ for $\mathit{N}$ molecules.

$\mathit{Work\; done}\mathsf{=}\mathit{p}\mathrm{∆}\mathit{V}$

Avogadro constant ${\mathit{N}}_{\mathrm{A}}$ , molar gas constant $\mathit{R}$ , Boltzmann constant $\mathit{k}$

Molar mass and molecular mass.

Required practical 8: Investigation of Boyle's law (constant temperature) and Charles’s law (constant pressure) for a gas.

Brownian motion as evidence for existence of atoms.

Explanation of relationships between $\mathit{p}$ , $\mathit{V}$ and $\mathit{T}$ in terms of a simple molecular model.

Students should understand that the gas laws are empirical in nature whereas the kinetic theory model arises from theory.

Assumptions leading to $\mathit{p}\mathit{V}\mathsf{=}\frac{\mathsf{1}}{\mathsf{3}}\mathit{N}\mathit{m}{\left({\mathit{c}}_{\mathrm{rms}}\right)}^{\mathsf{2}}\mathit{ }\mathit{ }$ including derivation of the equation and calculations.

A simple algebraic approach involving conservation of momentum is required.

Appreciation that for an ideal gas internal energy is kinetic energy of the atoms.

Use of average molecular kinetic energy = $\frac{\mathsf{1}}{\mathsf{2}}\mathit{m}{\left({\mathit{c}}_{\mathrm{r}\mathrm{m}\mathrm{s}}\right)}^{\mathsf{2}}\mathsf{=}\frac{\mathsf{3}}{\mathsf{2}}\mathit{k}\mathit{T}\mathsf{=}\frac{\mathsf{3}\mathit{R}\mathit{T}}{\mathsf{2}{\mathit{N}}_{\mathrm{A}}}$

Appreciation of how knowledge and understanding of the behaviour of a gas has changed over time.