## Angular Velocity and Linear Velocity – Class 11 | Chapter – 7 | Physics Short Notes Series PDF for NEET & JEE

Angular Velocity and Linear Velocity: Angular velocity and linear velocity are two different types of velocities that describe the motion of an object. Angular velocity describes the rotational motion of an object around an axis, while linear velocity describes the straight-line motion of an object. The two velocities are related to each other through the radius of rotation. Linear velocity, on the other hand, is a measure of how quickly an object is moving in a straight line. It is denoted by the symbol v and is expressed in units of meters per second (m/s).

## Angular Velocity and Linear Velocity

Angular velocity is a measure of how quickly an object is rotating around an axis. It is denoted by the symbol ω (omega) and is expressed in units of radians per second (rad/s). The formula for angular velocity is:

ω = Δθ / Δt

where Δθ is the change in the angle of rotation and Δt is the time taken for the rotation to occur. The direction of the angular velocity vector is perpendicular to the plane of rotation and follows the right-hand rule.

Linear velocity, on the other hand, is a measure of how quickly an object is moving in a straight line. It is denoted by the symbol v and is expressed in units of meters per second (m/s). The formula for linear velocity is:

v = Δs / Δt

where Δs is the change in position of the object and Δt is the time taken for the motion to occur. The direction of the linear velocity vector is in the direction of motion of the object.

While angular velocity and linear velocity are different types of velocities, they are related to each other through the radius of rotation. If an object is rotating around an axis with angular velocity ω and radius r, then the linear velocity of a point on the edge of the object is given by:

v = rω

This formula shows that the linear velocity of an object is directly proportional to its angular velocity and the radius of rotation.

## Relationship between Angular Velocity and Linear Velocity

The relationship between angular velocity and linear velocity can be described using the formula:

v = rω

where v is the linear velocity of a point on the edge of a rotating object, ω is the angular velocity of the object, and r is the distance from the axis of rotation to the point of interest.

This formula shows that the linear velocity of a point on a rotating object is directly proportional to the angular velocity of the object and the distance of the point from the axis of rotation.

The direction of the linear velocity vector is tangent to the circular path of the point on the edge of the rotating object, while the direction of the angular velocity vector is perpendicular to the plane of rotation and follows the right-hand rule.

## Difference between Angular Velocity and Linear Velocity

 Angular Velocity Linear Velocity Angular velocity is defined as the rate of change of the angular position of a rotating body. Linear velocity is defined as the rate of change of displacement with respect to time when the object moves along a straight path. When an object undergoes circular motion, the angular velocity of a particle is along the axis of a circle. Angular velocity remains the same. When an object undergoes circular motion, the linear velocity of a particle is along the circumference of a circle. Linear velocity varies at every point on the circle. The angular velocity is measured in degrees and radians. The linear velocity is measured in m/s. Angular velocity is represented by ω. Linear velocity is represented by v.

 JOIN OUR TELEGRAM CHANNELS Biology Quiz & Notes Physics Quiz & Notes Chemistry Quiz & Notes 