The angular velocity of a gar is controlled according to `omega=12-3t^(2)` where `omega` in radian per second, is positive in the clockwise sense and `t` is the time in seconds. Find the net angular displacement `triangletheta` from the time `t=0` to `t=3`s. Also, find the number of revolutions `N` through which the gear turns during the 3s.

Explanation

To solve the problem, we need to find the net angular displacement \(\Delta \theta\) from \(t = 0\) to \(t = 3\) seconds and the number of revolutions \(N\) the gear makes during this time.

### Step 1: Write down the expression for angular velocity
The angular velocity \(\omega\) is given by:
\[ \omega = 12 - 3t^2 \]

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