9702 · 12.2

Centripetal acceleration — practice questions

Practice and worked examples for 9702 Centripetal acceleration. Short previews only — attempt the full question in MarkScheme against the official scheme.

Worked example 1

A 0.50 kg mass is swung in a horizontal circle of radius 0.80 m at a constant linear speed of 4.0 m s⁻¹. Calculate: a) its centripetal acceleration, and b) the centripetal force acting on it.

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Identify knowns: $m = 0.50 \text{ kg}$ , $r = 0.80 \text{ m}$ , $v = 4.0 \text{ m s}^{-1}$ .
For centripetal acceleration ( $a_c$ ), use $a_c = \frac{v^2}{r}$ . $a_c = \frac{(4.0 \text{ m s}^{-1})^2}{0.80 \text{ m}} = \frac{16.0 \text{ m}^2 \text{ s}^{-2}}{0.80 \text{ m}} = 20 \text{ m s}^{-2}$ . So, $a_c = 20 \text{ m s}^{-2}$ .
For centripetal force ( $F_c$ ), use $F_c = m a_c$ . $F_c = (0.50 \text{ kg}) \times (20 \text{ m s}^{-2}) = 10 \text{ N}$ . So, $F_c = 10 \text{ N}$ .

Worked example 2

A car rounds a bend of radius 50 m at $12\,\text{m s}^{-1}$ . Calculate centripetal acceleration using $a = v^2/r$ and state what provides the centripetal force.

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$a = v^2/r = 12^2/50 = 2.9\,\text{m s}^{-2}$ (2 s.f.).

Friction between tyres and road provides the centripetal force $F = ma$ toward the centre.

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