A flywheel has a mass 200 kg and radius of gyration 0.6 m. It is given an angular speed of 150 rpm in 90 rotations starting from rest. Determine the torque assuming it to be constant that acted on the flywheel.

Explanation

To solve the problem step by step, we will determine the torque acting on the flywheel given its mass, radius of gyration, angular speed, and the number of rotations.

### Step 1: Convert Angular Speed from RPM to Radians per Second
The angular speed (ω) is given as 150 revolutions per minute (rpm). To convert this to radians per second, we use the conversion factor \(2\pi\) radians per revolution and divide by 60 seconds per minute.

\[ \omega = 150 \, \text{rpm} \times \frac{2\pi \, \text{radians}}{1 \, \text{revolution}} \times \frac{1 \, \text{minute}}{60 \, \text{seconds}} = 15.7 \, \text{radians/second} \]
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