Question

A car has wheels of radius $0.30m$ and is travelling at $36m/s$. Calculate :
(a) the angular speed of the wheel.
(b) If the wheels describe $40$ revolutions before coming to rest with a uniform acceleration.
(i) find it angular acceleration and
(ii) the distance covered.

Answer 1

Radius $r=0.30m$, Velocity, $v=36m/s$

$\left(a\right)$ angular speed $w=\frac{v}{r}=\frac{36}{0.3}=120rad/s$

$\left(b\right)$ final angular speed $w^{\prime }=0$

From rotational kinematics $w^{{}^{\prime }2}-w^2=2\alpha \theta 0-14400=2\alpha \times 40\times 2\pi \Rightarrow \alpha =\frac{-14400}{160\pi }=-28.6rad/s^2$

'Distance covered

$=40\times 2\pi r=40\times 2\pi \times 0.3=75.39m$