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

Answer

given,

initially rotating speed = 130 rad/s

final rotating speed = 0 rad/s

constant acceleration = 3 rad/s²

a)  using equation of rotating acceleration

   $\omega_f = \omega_i + \alpha t$

   $0 = 130 - 3 \times t$

    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

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

    $\theta = 130\times 43.33 - \dfrac{1}{2}\times 3 \times 43.33^2$

    $\theta = 2817 rad$

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