Question

A car with wheels of diameter 40 cm is accelerating from rest to 60 mi / hr over a period of 20 s. Find the angle, q, through which the tire has rotated.

Answer 1

Assume that the wheels are not slipping.

initial speed of car = 0

final speed = 60 mi/ hr = 26.8224 m/s

distance = average speed x time

$S=\frac{V+U}{2}\times t$

distance travelled by wheels is $S=\frac{26.8224+0}{2}\times 20=268.224\,m$

since wheel is not slipping $V=r\omega$ and hence $S=r\theta$ ( r is the radius of wheel = 0.20 m)

$268.224=0.20\times\theta$

$\theta = 1341^0$