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

Step-by-step 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+(1)/(2)\alpha t^2`

`565.48=753.98* 60+(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=(\omega_f-\omega_i)/(\alpha )`

`t=(0-753.98)/(-24.81)`

t = 30.39 seconds

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

`v=r* \omega_i`

`v=0.2* 753.98`

v = 150.79 m/s

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

`d=v* t`

`d=150.79\ m/s* 30.39\ s`

d = 4582.5 meters

or

d = 4.58 km