Starting from rest, a wheel undergoes constant angular acceleration for a period of time t. at what time after the start of rotation does the wheel reach an angular speed equal to its average angular speed for this interval?

At t=T/2 the angular speed equals to its average angular speed

Explanation:

Angular Motion

Let w be the angular speed of a rotating object, its angular acceleration, and T the time the acceleration is acting upon the object. The basic formula for the angular motion is

We are told the initial speed is zero, so

The average angular speed from t=0 to t=T can be found by

This value is reached at a certain time we need to compute, knowing that

Or equivalently

Simplifying we have

At t=T/2 the angular speed equals to its average angular speed