Question

A disk, initially rotating at 130 rad/s, is slowed down with a constant angular acceleration of magnitude 3.0 rad/s2.(a) How much time does the disk take to stop?

(b) Through what angle does the disk rotate during thattime?

Answer 1

given,

initially rotating speed = 130 rad/s

final rotating speed = 0 rad/s

constant acceleration = 3 rad/s²

a) using equation of rotating acceleration

`\omega_f = \omega_i + \alpha t`

`0 = 130 - 3 * t`

3 t = 130

t = 43.33 s

time does the disk take to stop is equal to 43.33 s

b) again using equation of rotation

`\theta = \omega_i t + (1)/(2)\alpha t^2`

`\theta = 130* 43.33 - (1)/(2)* 3 * 43.33^2`

`\theta = 2817 rad`

angle does the disk rotate during that time is equal to 2817 rad