The angular velocity of an object is given by the following equation: ω(t)=(5rads3)t2\omega\left(t\right) =\left(5\frac{rad}{s^3}\right)t^2ω( t)=(5s3rad​)t2 What is the angular displacement of the object (in rad) between t = 2 s and t = 4 s?

The angular displacement of the object between and is 20 radians.

Explanation:

The angular velocity of the object (), in radians per second, is given by the following expression:

(1)

Where is the time, measured in seconds.

The change in the angular displacement (), in radians, is found by means of the following definite integral:

(2)

Then we proceed to integrate on the function in time:

The angular displacement of the object between and is 20 radians.