How is angular velocity different from linear velocity?

Angular velocity refers to the rate of change of angular displacement, while linear velocity refers to the rate of change of linear displacement.

Angular velocity and linear velocity are two fundamental concepts in physics, particularly in the study of motion. They are different in their nature and the way they are measured and applied. Angular velocity, denoted by the symbol ω, is a measure of the rate of change of angular displacement with respect to time. It is typically measured in radians per second (rad/s) and is often used in the study of rotational motion, such as the spinning of a wheel or the rotation of a planet.

On the other hand, linear velocity, often denoted by the symbol v, is a measure of the rate of change of linear displacement with respect to time. It is typically measured in metres per second (m/s) and is used in the study of linear motion, such as the movement of a car along a straight road or a person walking across a room.

The relationship between angular and linear velocity can be understood through the formula v = rω, where v is the linear velocity, r is the radius of the circular path, and ω is the angular velocity. This formula shows that the linear velocity of an object moving in a circular path is directly proportional to both the radius of the path and the angular velocity of the object.

In summary, while both angular and linear velocity deal with the concept of 'speed', they apply to different types of motion. Angular velocity is concerned with the speed of rotation around a central point, while linear velocity deals with the speed of movement along a straight path. Understanding the difference between these two types of velocity is crucial for the study of physics, as it allows us to accurately describe and predict the behaviour of moving objects.