Question

. A grindstone increases in angular speed from 4.00 rad/s to 12.00 rad/s in 4.00 s. Through what angle does it turn during that time if the angular acceleration is constant?

Answer 1

Answer:

$\theta=32rad$

Explanation:

In an uniformly accelerated circular motion, the angle traveled by the object is given by:

$\theta=\frac{\omega_f+\omega_0}{2}t$

Here $\omega_f$ is the final angular speed, $\omega_0$ is the initial angular speed and t is the time of the motion. Replacing the given values:

$\theta=\frac{12\frac{rad}{s}+4\frac{rad}{s}}{2}(4s)\\\theta=32rad$