If angular momentum of a system is constant, which of the following will be zero

Options

A. force
B. torque
C. linear impulse
D. linear momentum

Answer

To solve the problem, we need to analyze the implications of the angular momentum of a system being constant.

### Step-by-Step Solution:

1. **Understanding Angular Momentum**:
Angular momentum (L) of a system is defined as the product of the moment of inertia (I) and the angular velocity (ω) of the system. Mathematically, it can be expressed as:
\[ L = I \cdot \omega \]

2. **Condition of Conservation**:
If the angular momentum is constant, it means that there is no net change in angular momentum over time. This can be expressed mathematically as:
\[ \frac{dL}{dt} = 0 \]
Here, \( \frac{dL}{dt} \) represents the rate of change of angular momentum with respect to time.

3. **Relation to Torque**:
According to the principle of rotational dynamics, the rate of change of angular momentum is equal to the net external torque (τ) acting on the system:
\[ \frac{dL}{dt} = \tau \]
Therefore, if \( \frac{dL}{dt} = 0 \), it implies:
\[ \tau = 0 \]
This means that the net external torque acting on the system is zero.

4. **Conclusion**:
Since the angular momentum is constant, the quantity that must be zero is the net external torque acting on the system. Thus, the answer to the question is that the torque will be zero.

### Final Answer:
If the angular momentum of a system is constant, the quantity that will be zero is the **torque**.

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