Question

A disc is rotated from rest about a vertical axis with an angular acceleration of 5.0 rads^-2 find the angular displacement of it's line of rotation

Answer 1

By the definition of the angular displacement, we have:

$$\theta=\omega_0t+\dfrac{1}{2}\alpha t^2.$$

Unfortunately, we don't know the time during which the disc accelerates. So, let's suppose that the disc is rotated from rest about a vertical axis with an angular acceleration 5.0 rads^-2 for 5 seconds, then the angular displacement of it's line of rotation equals:

$$\theta=\dfrac{1}{2}\cdot5\ \dfrac{rad}{s^2}\cdot(5.0\ s)^2=62.5\ rad.$$