Question

A rigid body acquires angular speed of 100 rad/s after undergoing angular displacement of 600 rad in 12 s. Find its constant angular acceleration and initial angular speed.

Answer 1

Answer:

$Angular\ acceleration\ =\ \dfrac{25}{6}\ rad/s$

initial angular speed = 50 rad/sec

Explanation:

Given,

Final angular speed, v = 100 rad/s

Displacement, s = 600 rad

time, t = 12 s

The initial angular speed can be given by,

$u\ =\ \dfrac{displacement}{time}$

    $=\ \dfrac{600}{12}$

    = 50 rad/s

Hence, the initial angular speed is 50 rad/s.

The angular acceleration can be given by,

$a\ =\ \dfrac{final\ angular\ spped\ -\ initial\ angular\ speed}{time}$

   $=\ \dfrac{100 - 50}{12}$

   $=\ \dfrac{50}{12}\ rad/s^2$

   $=\ \dfrac{25}{6}\ rad/s^2$

Hence, the angular acceleration is $\dfrac{25}{6}\ rad/s^2.$