A wheel is mounted on a stationary axle starts from rest and is given by the following angular acceleration : ` alpha = 9 - 12 t ` (in SI unit ) where t is the time after the wheel begins to rotate . Find the number of revolutions that the wheel turns before it stops ( and begins to turn in the opposite direction ) .

Explanation

To solve the problem step-by-step, we need to analyze the given angular acceleration and find the total angular displacement before the wheel stops and reverses its direction.

### Step 1: Understand the given angular acceleration
The angular acceleration is given by:
\[ \alpha = 9 - 12t \]
This means that the angular acceleration decreases linearly with time.
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