Question

A car has a top speed of 80 m/s (about 179 mi/h) and has wheels of radius 29 cm. If the car starts from rest and reaches its operating speed after 9.6 s, what is the angular acceleration of the wheels? Assume the car accelerates uniformly.

Answer 1

First we calculate the linear acceleration:

$a = \frac{v_f-v_i}{t} = \frac{0-80}{9.6}=-8.333 m/s^2$ in magnitude

a = 8.333 m/s²

the angular accleration is:

$\alpha = \frac{a}{R}=\frac{8.333}{0.29}=28.73 rad/s^2$