If a constant torque acts on a body, the body?

Options

A. will acquire a linear acceleration according to Newton's second law of motion
B. will acquire angular momentum
C. will rotate with a constant angular velocity
D. the body will move with a constant velocity or remain motion less in accordance with Newton's first law of motion.

Answer

To solve the question "If a constant torque acts on a body, the body?", we need to analyze the implications of a constant torque acting on a body in terms of its motion and angular momentum.

### Step-by-Step Solution:

1. **Understanding Torque**:
Torque (τ) is defined as the rotational equivalent of linear force. It is given by the formula:
\[ \tau = I \cdot \alpha \]
where \(I\) is the moment of inertia and \(\alpha\) is the angular acceleration.

2. **Constant Torque Implication**:
If a constant torque is acting on a body, it means that the torque value (τ) does not change over time. This implies that the angular acceleration (\(\alpha\)) will also remain constant because:
\[ \tau = I \cdot \alpha \implies \alpha = \frac{\tau}{I} \]
Since τ is constant and I is constant for a rigid body, \(\alpha\) must also be constant.

3. **Effect on Angular Velocity**:
Since the angular acceleration is constant, the angular velocity (\(\omega\)) of the body will change over time. The relationship between angular velocity and angular acceleration is given by:
\[ \omega = \omega_0 + \alpha t \]
where \(\omega_0\) is the initial angular velocity. This indicates that the body will not rotate with a constant angular velocity; instead, it will continuously increase its angular velocity.

4. **Angular Momentum Change**:
Angular momentum (L) is given by:
\[ L = I \cdot \omega \]
Since the angular velocity is changing due to the constant torque, the angular momentum will also change. The rate of change of angular momentum is equal to the torque:
\[ \tau = \frac{dL}{dt} \]
Therefore, if there is a constant torque, the angular momentum will also change, confirming that the body will acquire angular momentum.

5. **Linear Motion Consideration**:
The question also implies whether the body will acquire linear momentum or move with constant velocity. If a torque is acting on a body, it does not necessarily mean that a net force is acting on it. The body could be in a state of rotation without any linear acceleration if the net external forces are balanced. Thus, we cannot conclude that the body will acquire linear momentum or move with constant velocity.

### Conclusion:
From the analysis, we can conclude that if a constant torque acts on a body, the body will acquire angular momentum. Therefore, the correct answer is that the body will acquire angular momentum.