If the external torque acting on a system `vec(tau)=0` then

Options

A. `omega=0`
B. `alpha=0`
C. `J=0`
D. `F=0`

Explanation

To solve the question, "If the external torque acting on a system \(\vec{\tau} = 0\) then...", we need to analyze the implications of zero external torque in the context of rotational motion.

### Step-by-Step Solution:

1. **Understanding Torque and Angular Acceleration**:
- Torque (\(\tau\)) is related to angular acceleration (\(\alpha\)) by the equation:
\[ \tau = I \cdot \alpha \]
where \(I\) is the moment of inertia of the object.

2. **Setting External Torque to Zero**:
- Given that the external torque \(\tau = 0\), we can substitute this into the equation:
\[ 0 = I \cdot \alpha \]

3. **Analyzing the Equation**:
- Since the moment of inertia \(I\) is always a positive value for any physical object (it cannot be zero), the only way for the product \(I \cdot \alpha\) to equal zero is if:
\[ \alpha = 0 \]
- This means that the angular acceleration of the system is zero.

4. **Implications of Zero Angular Acceleration**:
- If \(\alpha = 0\), it indicates that the angular velocity (\(\omega\)) of the system is constant. The system is either at rest or moving with a constant angular velocity.

5. **Conclusion**:
- Therefore, if the external torque acting on a system is zero, we can conclude that:
- The angular acceleration \(\alpha\) is zero.
- The angular velocity \(\omega\) remains constant (it can be zero or any constant value).

### Final Answer:
If the external torque acting on a system \(\vec{\tau} = 0\), then the angular acceleration \(\alpha = 0\) and the angular velocity \(\omega\) is constant.

---