The angle covered by the grindstone during this time is, converting into radians,
[tex]\theta = 20 rev = 20 rev \cdot \frac{2 \pi rad}{rev} =125. 6rad[/tex]
This is a rotational motion with constant angular acceleration [tex]\alpha[/tex], and with initial angular speed [tex]\omega _0 =0[/tex]. The angle covered in a time t is given by
[tex]\theta (t)= \omega_0 t+ \frac{1}{2} \alpha t^2 = \frac{1}{2} \alpha t^2 [/tex]
because the initial angular speed is zero.
Using t=8.00 s, we can find the value of angular acceleration:
[tex]\alpha = \frac{2 \theta}{t^2}= \frac{2 \cdot 125.6 rad}{(8.0 s)^2}=3.93 rad/s^2 [/tex]
