The direction of angular acceleration of a body moving in a circle in the plane of the paper is .

Options

A. perpendicular to radius and velocity
B. towards the radius
C. tangential
D. at right angle to angular velocity

Answer

To determine the direction of angular acceleration of a body moving in a circle in the plane of the paper, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Angular Acceleration**:
Angular acceleration (\( \alpha \)) is defined as the rate of change of angular velocity (\( \omega \)) with respect to time. It can be positive or negative depending on whether the angular velocity is increasing or decreasing.

2. **Visualizing the Motion**:
Consider a particle moving in a circular path in the plane of the paper. Let’s denote the radius of the circle as \( r \) and the velocity of the particle as \( v \).

3. **Direction of Angular Velocity**:
The direction of angular velocity (\( \omega \)) can be determined using the right-hand rule. If you curl the fingers of your right hand in the direction of the particle's motion, your thumb will point in the direction of the angular velocity vector, which is perpendicular to the plane of motion.

4. **Determining Angular Acceleration**:
- If the particle's speed is increasing, the angular acceleration will be in the same direction as the angular velocity (out of the plane).
- If the particle's speed is decreasing, the angular acceleration will be in the opposite direction to the angular velocity (into the plane).

5. **Using the Right-Hand Rule**:
To find the direction of angular acceleration, use the right-hand rule:
- Curl your fingers in the direction of the velocity vector.
- Your thumb will point in the direction of the angular velocity.
- If the velocity increases, the angular acceleration is out of the plane (thumb points out).
- If the velocity decreases, the angular acceleration is into the plane (thumb points in).

6. **Conclusion**:
The direction of angular acceleration of a body moving in a circle in the plane of the paper can either be into the plane or out of the plane, depending on whether the angular velocity is decreasing or increasing, respectively.