When a constant torque is applied, a wheel is turned from rest through 200 radians in 10 s. What is its angular acceleration. If the same torque continues to act what is the angular velocity of the wheel after 15 s from the start ?

Explanation

To solve the problem step by step, we will follow the physics principles related to angular motion.

### Step 1: Identify the given values
- Initial angular velocity (\( \omega_0 \)) = 0 rad/s (since it starts from rest)
- Angular displacement (\( \theta \)) = 200 radians
- Time (\( t \)) = 10 seconds

### Step 2: Use the angular motion equation
We can use the equation of motion for angular displacement:
\[ \theta = \omega_0 t + \frac{1}{2} \alpha t^2 \]
Since the initial angular velocity (\( \omega_0 \)) is 0, the equation simplifies to:
\[ \theta = \frac{1}{2} \alpha t^2 \]

### Step 3: Solve for angular acceleration (\( \alpha \))
Rearranging the equation to solve for \( \alpha \):
\[ \alpha = \frac{2\theta}{t^2} \]
Substituting the known values:
\[ \alpha = \frac{2 \times 200 \text{ rad}}{(10 \text{ s})^2} = \frac{400 \text{ rad}}{100 \text{ s}^2} = 4 \text{ rad/s}^2 \]

### Step 4: Find the angular velocity after 15 seconds
Now, we need to find the angular velocity after 15 seconds using the formula:
\[ \omega = \omega_0 + \alpha t \]
Substituting the known values:
\[ \omega = 0 + (4 \text{ rad/s}^2) \times (15 \text{ s}) = 60 \text{ rad/s} \]

### Final Answers
- The angular acceleration (\( \alpha \)) is \( 4 \text{ rad/s}^2 \).
- The angular velocity after 15 seconds (\( \omega \)) is \( 60 \text{ rad/s} \).

---