Question

The wheel of a car has a radius of 20.0 cm. It initially rotates at 120 rpm. In the next minute it makes 90.0 revolutions. (a) What is the angular acceleration? (b) How much further does the car travel before coming to rest? There is no slipping.

Answer 1

Answer:

Explanation:

Given that,

Radius of the wheel, r = 20 cm = 0.2 m

Initial speed of the wheel, $\omega_i=120\ rpm=753.98\ rad/s$

Displacement, $\theta=90\ rev=565.48\ rad$

To find,

The angular acceleration and the distance covered by the car.

Solution,

Let $\alpha$ is the angular acceleration of the car. Using equation of rotational kinematics as :

$\theta=\omega_i t+\dfrac{1}{2}\alpha t^2$

$565.48=753.98\times 60+\dfrac{1}{2}\alpha (60)^2$

$\alpha =-24.81\ rad/s^2$

Let t is the time taken by the car before coming to rest.

$t=\dfrac{\omega_f-\omega_i}{\alpha }$

$t=\dfrac{0-753.98}{-24.81}$

t = 30.39 seconds

Let v is the linear velocity of the car. So,

$v=r\times \omega_i$

$v=0.2\times 753.98$

v = 150.79 m/s

Let d is the distance covered by the car. It can be calculated as :

$d=v\times t$

$d=150.79\ m/s\times 30.39\ s$

d = 4582.5 meters

or

d = 4.58 km