Question

A Wheel initially rotating at an angular velocity of 15.0 rad/s is decelerating at a rate of 2.0 rad/s². How many revolutions will the wheel make before coming to rest?

Answer 1

Initial angular velocity 1 = 15 rad/s

And final angular velocity 2  = 0 rad/s because it is coming to rest.

And angular acceleration = - 2 rad/s2

Negative sign indicates deceleration

Now, angular displacement ​​​​​​ is

(2)2 = ( 1​​​​​​)2 + 2

0 = 225 + 2(-2)

Therefore,   = 225/4 = 56.25 rad

Now

Numbers of revolution "n" is

n = /2

Where, = 3.14

n = (56.25)/(2×3.14)

n = 8.957 revolutions,

n 9 revolutions

9 revolution will the wheel make before coming to the rest.