A wheel of mass 10 kg and radius 0.2 m is rotating at an angular speed of 100 rpm, when the motion is turned off. Neglecting the friction at the axis. Calculate the force that must be applied tangentially to the wheel to bring it to rest in 10 rev. Assumed wheel to be a disc.

Explanation

To solve the problem step by step, we will follow these steps:

### Step 1: Convert Angular Speed from RPM to Radians per Second
The initial angular speed \( \omega_0 \) is given as 100 RPM. We need to convert this to radians per second.

\[ \omega_0 = 100 \, \text{RPM} \times \frac{2\pi \, \text{radians}}{1 \, \text{revolution}} \times \frac{1 \, \text{minute}}{60 \, \text{seconds}} = \frac{100 \times 2\pi}{60} \, \text{radians/second} = \frac{100\pi}{30} \, \text{radians/second} \approx 10.47 \, \text{radians/second} \]
...