The moment of inertia of a flywheel is `4 kg m^(2)`. What angular acceleration will be produced in it by applying a torque of 10 Nm on it?

Answer

To find the angular acceleration produced in the flywheel when a torque is applied, we can use the relationship between torque (τ), moment of inertia (I), and angular acceleration (α). The formula is given by:

\[ \tau = I \alpha \]

Where:
- \( \tau \) is the torque applied (in Nm),
- \( I \) is the moment of inertia (in kg m²),
- \( \alpha \) is the angular acceleration (in rad/s²).

### Step-by-Step Solution:

1. **Identify the given values**:
- Moment of inertia, \( I = 4 \, \text{kg m}^2 \)
- Torque applied, \( \tau = 10 \, \text{Nm} \)

2. **Use the formula for torque**:
\[ \tau = I \alpha \]
Rearranging the formula to solve for angular acceleration \( \alpha \):
\[ \alpha = \frac{\tau}{I} \]

3. **Substitute the known values into the equation**:
\[ \alpha = \frac{10 \, \text{Nm}}{4 \, \text{kg m}^2} \]

4. **Calculate the angular acceleration**:
\[ \alpha = \frac{10}{4} = 2.5 \, \text{rad/s}^2 \]

### Final Answer:
The angular acceleration produced in the flywheel by applying a torque of 10 Nm is \( 2.5 \, \text{rad/s}^2 \).

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