Centripetal acceleration of a ball

Problem

A ball travels round a circle of radius $r = 40\;\text{cm}$ at constant speed $v = 2{,}0\;\text{m/s}$. Calculate the centripetal acceleration.

Solution

Data. $r = 40\;\text{cm} = 0{,}40\;\text{m}$, $v = 2{,}0\;\text{m/s}$.

Centripetal acceleration formula. In uniform circular motion the magnitude of the velocity is constant, but its direction changes: the acceleration points towards the centre and is given by $a_c = \frac{v^2}{r}$

Numerical substitution (careful: the radius must be in metres): $a_c = \frac{(2{,}0)^2}{0{,}40} = \frac{4{,}0}{0{,}40} = 10\;\text{m/s}^2$

Result. $\ev{a_c = 10\;\text{m/s}^2}$

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Topics: Dinamica Concepts: Moto circolare uniforme · Accelerazione centripeta