The moment of inertia of a body is `2.5 kg m^(2)`. Calculate the torque required to produce an angular acceleration of `18 rad s^(-2)` in the body.

Answer

To calculate the torque required to produce an angular acceleration in the body, we can use the formula:

\[ \tau = I \cdot \alpha \]

where:
- \(\tau\) is the torque,
- \(I\) is the moment of inertia,
- \(\alpha\) is the angular acceleration.

### Step-by-Step Solution:

1. **Identify the given values:**
- Moment of inertia, \(I = 2.5 \, \text{kg m}^2\)
- Angular acceleration, \(\alpha = 18 \, \text{rad/s}^2\)

2. **Substitute the values into the torque formula:**
\[ \tau = I \cdot \alpha = 2.5 \, \text{kg m}^2 \cdot 18 \, \text{rad/s}^2 \]

3. **Perform the multiplication:**
\[ \tau = 2.5 \cdot 18 = 45 \, \text{N m} \]

4. **State the final answer:**
The torque required to produce an angular acceleration of \(18 \, \text{rad/s}^2\) in the body is \(45 \, \text{N m}\).