Total angular momentum of a rotating body remains constant, if the net torque acting on the body is

Options

A. zero
B. maximum
C. minimum
D. unity

Explanation

To solve the question, we need to understand the relationship between angular momentum and torque. Here is the step-by-step solution:

### Step-by-Step Solution:

1. **Understanding Angular Momentum (L)**:
- Angular momentum (L) of a rotating body is a measure of the amount of rotation it has, taking into account its mass distribution and rotational speed.

2. **Understanding Torque (τ)**:
- Torque (τ) is a measure of the force that causes an object to rotate about an axis. It is defined as the rate of change of angular momentum.

3. **Relationship Between Torque and Angular Momentum**:
- The relationship between torque and angular momentum can be expressed mathematically as:
\[ \tau = \frac{dL}{dt} \]
- This equation states that torque is equal to the derivative of angular momentum with respect to time.

4. **Condition for Constant Angular Momentum**:
- If the total angular momentum (L) of a rotating body remains constant, it means that there is no change in angular momentum over time.
- Mathematically, if L is constant, then:
\[ \frac{dL}{dt} = 0 \]

5. **Implication for Torque**:
- From the equation \(\tau = \frac{dL}{dt}\), if \(\frac{dL}{dt} = 0\), then it follows that:
\[ \tau = 0 \]
- This means that the net torque acting on the body must be zero for the angular momentum to remain constant.

6. **Conclusion**:
- Therefore, the total angular momentum of a rotating body remains constant if the net torque acting on the body is zero.

### Final Answer:
The total angular momentum of a rotating body remains constant if the net torque acting on the body is **zero**.

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