If the torque on a body is zero, then?

Options

A. `Jomega=constant`
B. `Iomega=constant`
C. `(Iomega^2)/2=constant`
D. `(mv^2)/2=constant`

Answer

To solve the question "If the torque on a body is zero, then?" we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Torque**:
- Torque (\( \tau \)) is defined as the rate of change of angular momentum (\( L \)). Mathematically, this is expressed as:
\[ \tau = \frac{dL}{dt} \]

2. **Setting Torque to Zero**:
- According to the problem, the torque on the body is zero:
\[ \tau = 0 \]

3. **Implication of Zero Torque**:
- If the torque is zero, then the rate of change of angular momentum must also be zero:
\[ \frac{dL}{dt} = 0 \]
- This implies that the angular momentum (\( L \)) is constant over time.

4. **Relating Angular Momentum to Moment of Inertia and Angular Velocity**:
- Angular momentum can be expressed in terms of moment of inertia (\( I \)) and angular velocity (\( \omega \)):
\[ L = I \cdot \omega \]

5. **Conclusion**:
- Since \( L \) is constant and \( L = I \cdot \omega \), it follows that the product of moment of inertia and angular velocity must also be constant. Therefore, if the moment of inertia changes, the angular velocity must change in such a way that their product remains constant.

### Final Answer:
If the torque on a body is zero, then the angular momentum of the body is constant, which implies that the product of moment of inertia and angular velocity is also constant.

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