Edexcel A-Level Physics Centripetal Acceleration

Practise Edexcel A-Level Physics centripetal acceleration by deriving v squared over r and applying circular-motion equations.

Exam points

derive centripetal acceleration from velocity vector diagrams and small-angle geometry
calculate centripetal acceleration from frequency, radius, speed or angular velocity

[Maximum number: 5]

An aeroplane flies in a horizontal circular path whilst waiting to land at an airport.

The aeroplane flies at a constant speed v around a horizontal circular path of radius r. The diagram shows two positions A and B of the aeroplane, on its circular path.

Figure for Question 4.3.89 - Centripetal acceleration derivation question 1 — Edexcel A-Level Physics A2

The acceleration of the aeroplane is a.
Derive the expression $a=\frac{v^{2}}{r}$
You should include a vector diagram.

For a small angular displacement, the velocity-vector triangle gives $\Delta v/v\approx\theta$ . Also $v=r\theta/t$ , so $\theta/t=v/r$ . Therefore $a=\frac{\Delta v}{t}=v\frac{\theta}{t}=\frac{v^2}{r}.$

Figure for Answer to Question 4.3.89 - Centripetal acceleration derivation question 1 — Edexcel A-Level Physics A2

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4.3.89 - Centripetal acceleration derivation question 1