Edexcel A-Level Physics 9PH0
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Further Mechanics
Centripetal acceleration
- 1 thing to know
- Papers 1 and 3
Overview
Recall questions on why circular motion at constant speed is accelerated, the direction of the acceleration, the two equations, and how each responds to a change of speed or radius.
What you need to know
Answer each one before you reveal it.
Questions from this subtopic
Each one with the model answer underneath.
- 1
Why is an object moving in a circle at constant speed still accelerating?
Model answer
Velocity is a vector and its direction changes continuously, so the velocity is changing and there must be an acceleration.
- 2
In which direction does centripetal acceleration act?
Model answer
It acts towards the centre of the circular path, at right angles to the instantaneous velocity.
- 3
How does a vector diagram of the velocities at two nearby points lead to the equation for centripetal acceleration?
Model answer
The two velocity vectors, equal in magnitude v and separated by a small angle Δθ, form an isosceles triangle in which the change of velocity has magnitude Δv = vΔθ; dividing by Δt gives a = v(Δθ/Δt) = vω, and substituting v = ωr gives a = v²/r.
- 4
In a vector diagram of the velocities at two nearby points on a circular path, why does the change in velocity point towards the centre of the circle?
Model answer
For a very small angle the vector difference between the two velocities lies almost perpendicular to both of them, which is along the radius directed inwards.
- 5
State the two equations for centripetal acceleration:
Model answer
The centripetal acceleration is a = v²/r and equivalently a = rω².
- 6
How can the two expressions for centripetal acceleration be shown to be equivalent?
Model answer
Substituting v = ωr into v²/r gives (ωr)²/r = ω²r²/r = rω².
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