A body moves with constant angular velocity on a circle. Magnitude of angular acceleration

Options

A. `r omega`
B. Constant
C. Zero
D. None of the above

Answer

To solve the problem of finding the magnitude of angular acceleration for a body moving with constant angular velocity on a circle, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Angular Velocity**:
- Angular velocity (ω) is defined as the rate of change of angular displacement. In this case, it is given that the body moves with a constant angular velocity.

2. **Definition of Angular Acceleration**:
- Angular acceleration (α) is defined as the rate of change of angular velocity with respect to time. Mathematically, it is expressed as:
\[ \alpha = \frac{d\omega}{dt} \]

3. **Constant Angular Velocity**:
- Since the problem states that the body is moving with a constant angular velocity, this means that ω does not change over time. Therefore, we can say:
\[ \omega = \text{constant} \]

4. **Calculating Angular Acceleration**:
- Now, if ω is constant, the derivative of a constant with respect to time is zero. Thus, we can write:
\[ \alpha = \frac{d\omega}{dt} = 0 \]

5. **Conclusion**:
- Since the angular acceleration (α) is zero, we conclude that the magnitude of angular acceleration is:
\[ |\alpha| = 0 \]

### Answer:
The magnitude of angular acceleration is **0**.

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