Question

A centrifuge accelerates from rest to 1571 radians per second in 250s. Through what angular displacement did it turn in this time?

Answer 1

When a centrifuge accelerates from rest to 1571 rad/s in 250 s, the angular displacement was

$$\phi=\frac{(\omega_f-\omega_i)t}{2}=\frac{(1571-0)250}{2}=196375\text{ rad}=\\=62508.1\pi.$$