The correct relation between linear velocity `overset rarr(v)` and angular velocity `overset rarr(omega)` of a particle is

Options

A. `vecv=vecr xx vecomega`
B. `vecv=vecomega xx vecr`
C. `vecomega=vecr xx vecv`
D. `vecomega= vecv xx vecr`

Explanation

To find the correct relation between linear velocity \(\vec{v}\) and angular velocity \(\vec{\omega}\) of a particle, we can follow these steps:

### Step 1: Understand the Definitions
- **Linear Velocity (\(\vec{v}\))**: This is the rate of change of displacement of a particle. It is a vector quantity that has both magnitude and direction.
- **Angular Velocity (\(\vec{\omega}\))**: This is the rate of change of angular displacement of a particle. It also is a vector quantity.

### Step 2: Relate Linear and Angular Velocity
For a particle moving in a circular path of radius \(r\), the relationship between linear velocity and angular velocity can be expressed mathematically. The linear velocity \(\vec{v}\) is related to the angular velocity \(\vec{\omega}\) by the formula:
\[ \vec{v} = r \cdot \vec{\omega} \]
where:
- \(r\) is the radius of the circular path,
- \(\vec{\omega}\) is the angular velocity vector.

### Step 3: Magnitude of the Relation
If we consider the magnitudes of the vectors, we can express the relationship as:
\[ v = r \cdot \omega \]
This means that the linear velocity is equal to the radius multiplied by the angular velocity.

### Step 4: Conclusion
Thus, the correct relation between linear velocity \(\vec{v}\) and angular velocity \(\vec{\omega}\) of a particle is:
\[ \vec{v} = r \cdot \vec{\omega} \]