Define angular velocity and angular acceleration. Obtain relation between linear velocity and angular velocity.

Angular velocity refers to the rate at which an object rotates around a specific axis. It is defined as the change in angular displacement per unit of time. Angular velocity is typically represented by the Greek letter omega (ω) and is measured in radians per second (rad/s).

Angular acceleration, on the other hand, refers to the rate at which the angular velocity of an object changes with respect to time. It is defined as the change in angular velocity per unit of time. Angular acceleration is denoted by the Greek letter alpha (α) and is measured in radians per second squared (rad/s²).

The relationship between linear velocity (v) and angular velocity (ω) depends on the distance of a point from the axis of rotation. This distance is often represented by the letter "r" and is known as the radius or the distance from the axis of rotation to the point in question.

The formula to relate linear velocity and angular velocity is:

v = r * ω

where:

v is the linear velocity in meters per second (m/s).
r is the radius or distance from the axis of rotation to the point in question in meters (m).
ω is the angular velocity in radians per second (rad/s).
This formula shows that the linear velocity of a point on a rotating object is directly proportional to the distance of that point from the axis of rotation and the angular velocity of the object. Essentially, the linear velocity increases as the radius or distance from the axis of rotation increases, and it also increases as the angular velocity increases.