Question

A car accelerates uniformly from rest to a speed of 15 m/s in a time of 20s. Find the angular acceleration of one of it wheels and the number of revolutions turned by a wheel in the process. The radius of the car is 1/3 m.

Answer 1

Given :

Final velocity of the car = 15 m/s

Time period = 20 sec

Radius of the car tires = 1/3 m

To Find :

Angular acceleration of the wheels

Number of revolutions turned by the wheel

Solution :

• From equations of motion,  $v=u+at$

• By substutiting the values we get

         $v=u+at$

         $15=0+a\times 20$

         $a= \frac{3}{4} m/s^{2}$

• Distance travelled by the car is

         $s=ut+\frac{1}{2}at^{2}$

         $s=0\times 20+\frac{1}{2}\frac{3}{4}\times 20^{2}$

         $s=50m$

• The number of revolutions made by wheel is calucated as

         $Distance=s=n\times 2\pi r$

         $n = \frac{s}{2\pi r}$

         $n = \frac{50}{2\times 3.14 \times \frac{1}{3} }$

         $n = 23.88rev$

Total number of revolutions made by the wheel is 23.88 rev

• Angular acceleration is given by the formula $v=r\omega$

         $\omega = \frac{v}{r}$

         $\omega = \frac{15}{\frac{1}{3} }$

         $\omega = 45 rad /s = \frac{45}{2\pi } rev / s$

         $\omega = 7.15 rev/sec$

Angular acceleration of the wheel is 7.15 rev/s