If angular velocity of a disc depends an angle rotated `theta` as `omega=theta^(2)+2theta`, then its angular acceleration `alpha` at `theta=1` rad is :

Options

A. `4" rad/s"^(2)`
B. `10" rad/s"^(2)`
C. `12" rad/s"^(2)`
D. `15" rad/s"^(2)`

Explanation

To solve the problem, we need to find the angular acceleration \( \alpha \) at \( \theta = 1 \) radian, given that the angular velocity \( \omega \) is defined as:

\[ \omega = \theta^2 + 2\theta \]

### Step 1: Understand the relationship between angular acceleration and angular velocity
Angular acceleration \( \alpha \) is defined as the rate of change of angular velocity with respect to time, which can be expressed as:
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