The relation between linear speed v, angular speed `omega` and angular acceleration `alpha` in circular motion is

Options

A. `alpha=(aomega)/v`
B. `alpha=(av)/omega`
C. `alpha=(vomega)/a`
D. `alpha=(omega)/(av)`

Answer

To establish the relationship between linear speed \( v \), angular speed \( \omega \), and angular acceleration \( \alpha \) in circular motion, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Linear Speed and Angular Speed**:
- Linear speed \( v \) is the speed of an object moving along a circular path.
- Angular speed \( \omega \) is the rate of change of angular displacement and is measured in radians per second.

2. **Relationship between Linear Speed and Angular Speed**:
- The linear speed \( v \) of an object in circular motion is related to its angular speed \( \omega \) by the formula:
\[ v = r \cdot \omega \]
where \( r \) is the radius of the circular path.

3. **Understanding Angular Acceleration**:
- Angular acceleration \( \alpha \) is the rate of change of angular speed and is measured in radians per second squared.

4. **Relationship between Linear Acceleration and Angular Acceleration**:
- The linear acceleration \( a \) of an object in circular motion can be related to angular acceleration \( \alpha \) using the formula:
\[ a = r \cdot \alpha \]
This means that if the angular speed is changing, the linear acceleration can be calculated by multiplying the radius by the angular acceleration.

5. **Summary of Relationships**:
- The relationships can be summarized as:
- \( v = r \cdot \omega \) (linear speed and angular speed)
- \( a = r \cdot \alpha \) (linear acceleration and angular acceleration)

### Final Relationships:
- The relationship between linear speed \( v \), angular speed \( \omega \), and angular acceleration \( \alpha \) in circular motion can be expressed as:
\[ v = r \cdot \omega \]
\[ a = r \cdot \alpha \]