A grind-stone is in the form of a solid cylinder has a radius of 0.5 m and a mass 50 kg. What torque will bring it from rest to an angular velocity of 300 rev/min in 10 s ? What is the kinetic energy when it is rotating at 300 rev/min ?

Explanation

To solve the problem step by step, we will find the torque required to bring the grindstone from rest to an angular velocity of 300 revolutions per minute (rev/min) in 10 seconds, and then calculate the kinetic energy when it is rotating at that speed.

### Step 1: Convert Angular Velocity from rev/min to rad/s
First, we need to convert the final angular velocity from revolutions per minute to radians per second.

\[ \omega = 300 \, \text{rev/min} \times \frac{2\pi \, \text{rad}}{1 \, \text{rev}} \times \frac{1 \, \text{min}}{60 \, \text{s}} = 300 \times \frac{2\pi}{60} = 10\pi \, \text{rad/s} \]
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