CCEA A Level Physics
CCEA A Level Physics 4.3 Uniform Circular Motion and 4.4 Simple Harmonic Motion Exam Questions
Free CCEA A Level Physics revision for 4.3 Uniform Circular Motion and 4.4 Simple Harmonic Motion: what you need to know, common mistakes and exam-style questions with answers. Covers angular velocity, v = rω, centripetal force, simple harmonic motion, a = -ω^2x, pendulums, springs, resonance and damping.
Practise 4.3 Uniform Circular Motion and 4.4 Simple Harmonic Motion with past papers
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About CCEA A Level Physics 4.3 Uniform Circular Motion and 4.4 Simple Harmonic Motion
These sections of Unit A2 1: Deformation of Solids, Thermal Physics, Circular Motion, Oscillations and Atomic and Nuclear Physics deal with repeating motion. Circular motion introduces angular velocity and the centripetal force needed to keep an object on a circular path. Simple harmonic motion is defined by a = -ω^2x, with displacement x = A cos ωt, and is investigated using a simple pendulum and a mass on a spiral spring. You also need SHM graphs, free and forced vibrations, resonance and the three kinds of damping. Typical questions ask for the source of a centripetal force, SHM calculations of maximum speed and acceleration, and sketches of resonance curves.
What you need to know
- Angular velocity ω = Δθ/Δt in rad s-1, ω = 2π/T = 2πf, and linear speed v = rω.
- Centripetal force An object moving in a circle at constant speed accelerates towards the centre with a = v^2/r = rω^2. The resultant force needed is F = mv^2/r = mrω^2, provided by tension, friction, gravity or a normal force.
- Defining SHM Acceleration is proportional to displacement from equilibrium and directed towards it: a = -ω^2x. Displacement x = A cos ωt when timing starts at maximum displacement.
- Speed and acceleration Maximum speed is ωA at the equilibrium position; maximum acceleration is ω^2A at the extremes. Velocity-time and acceleration-time graphs are a quarter and half cycle out of phase with displacement.
- Pendulum and spring Simple pendulum T = 2π square root of (l/g) for small angles; mass on a spring T = 2π square root of (m/k). Time several oscillations and repeat to reduce uncertainty.
- Forced vibrations and damping Resonance occurs when the driving frequency equals the natural frequency, giving maximum amplitude. Light damping gives a slow decay; critical damping returns to equilibrium in the shortest time without oscillating; over-damping returns slowly without oscillating.
Common mistakes in 4.3 Uniform Circular Motion and 4.4 Simple Harmonic Motion
- Adding centripetal force as an extra force on a diagram; it is the resultant of the real forces acting.
- Saying an object in uniform circular motion has no acceleration; its velocity changes direction, so it accelerates towards the centre.
- Leaving out the minus sign in a = -ω^2x, which shows the acceleration is opposite to the displacement.
- Thinking the period of a pendulum depends on its mass; it depends only on length and g for small oscillations.
- Describing critical damping as stopping as fast as possible; it is the fastest return to equilibrium without oscillating.
Try three 4.3 Uniform Circular Motion and 4.4 Simple Harmonic Motion exam-style questions
1. A car of mass 1200 kg travels round a bend of radius 50 m at 15 m s-1. Calculate the centripetal force needed. (2 marks)
Show the mark scheme answer
F = mv^2/r = 1200 x 15^2 / 50; = 5400 N.
2. An object oscillates with SHM of amplitude 0.050 m and frequency 2.0 Hz. Calculate its maximum speed and maximum acceleration. (3 marks)
Show the mark scheme answer
ω = 2πf = 12.6 rad s-1; v(max) = ωA = 12.6 x 0.050 = 0.63 m s-1; a(max) = ω^2A = 158 x 0.050 = 7.9 m s-2.
3. Describe how a simple pendulum can be used to show that T is proportional to the square root of l. (4 marks)
Show the mark scheme answer
Measure length to the centre of the bob for several lengths; time 20 oscillations with small amplitude and repeat; calculate T; plot T^2 against l; a straight line through the origin confirms the relationship (gradient 4π^2/g).
4.3 Uniform Circular Motion and 4.4 Simple Harmonic Motion FAQs
What does CCEA A Level Physics 4.3 and 4.4 cover?
Angular velocity and centripetal force for uniform circular motion, then simple harmonic motion, pendulum and spring experiments, SHM graphs, forced vibrations, resonance and damping.
Which unit are 4.3 and 4.4 examined in?
Both are in Unit A2 1: Deformation of Solids, Thermal Physics, Circular Motion, Oscillations and Atomic and Nuclear Physics.
How do I recognise a SHM question?
Look for an oscillation where the restoring acceleration is proportional to displacement. Find ω first from the period or frequency, then use ωA and ω^2A for maximum speed and acceleration.
