A centrifuge in a medical laboratory rotates at a rotational speed of 3600 rev/min. When turned off, it rotates 20.0 times at a constant angular acceleration before coming to rest. The angle through which the centrifuge rotates before coming to rest is
A) 3.18 rad.
B) 20.0 rad.
C) 80.0 rad.
D) 126 rad.
E) 180 rad.

Question

Quizplus · Accepted Answer

The angle through which the centrifuge rotates before coming to rest can be calculated using the formula for the angle of rotation $\theta$ in radians during a deceleration process: $\theta = \frac{1}{2}(\omega_0 + \omega)t$, where $\omega_0$ is the initial angular velocity, $\omega$ is the final angular velocity (which is 0 since it comes to rest), and $t$ is the time. However, since we are not given time and the angular acceleration is constant, we can use another approach by converting the given rotations into radians (since 1 rotation = $2\pi$ radians) and then directly calculating the angle. Given that it rotates 20.0 times before coming to rest, the total angle in radians is $20.0 \times 2\pi = 40\pi \approx 126$ radians.

A Centrifuge in a Medical Laboratory Rotates at a Rotational