A wheel has a speed of 1200 revolution per minute and is made to slow down at a rate of 4 radian/`s^(2)`. The number of revolutions it makes before coming to rest is

Explanation

To solve the problem step by step, we will follow the approach outlined in the video transcript.

### Step 1: Convert the initial speed from revolutions per minute to radians per second
The initial speed of the wheel is given as 1200 revolutions per minute (rpm). To convert this to radians per second, we use the conversion factor that \(1 \text{ revolution} = 2\pi \text{ radians}\) and \(1 \text{ minute} = 60 \text{ seconds}\).

\[ \omega_{\text{initial}} = 1200 \, \text{rev/min} \times \frac{2\pi \, \text{radians}}{1 \, \text{rev}} \times \frac{1 \, \text{min}}{60 \, \text{s}} = 1200 \times \frac{2\pi}{60} = 40\pi \, \text{radians/s} \]
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