Angular Velocity

Angular velocity is a measure of the rate of change of angular displacement of a rotating object. It is a vector quantity, with both magnitude and direction, and is expressed in units of radians per second (rad/s) or degrees per second (°/s).

Formula for Angular Velocity

The formula for angular velocity (ω) is given by:

ω = Δθ / Δt

Where ω is the angular velocity, Δθ is the change in angular displacement, and Δt is the change in time.

Units of Angular Velocity

Angular velocity is typically measured in radians per second (rad/s) or degrees per second (°/s).

Relationship between Linear and Angular Velocity

There is a relationship between linear velocity (v) and angular velocity (ω) for a rotating object. This relationship is given by:

v = rω

Where v is the linear velocity, r is the radius of the circular path, and ω is the angular velocity.

Applications of Angular Velocity

Angular velocity is used to describe the speed of rotation of objects such as wheels, gears, and other rotating machinery. It is also important in the study of rotational motion in physics and engineering.

Study Guide

1. What is angular velocity and how is it different from linear velocity?
2. What are the units of angular velocity?
3. How is angular velocity related to linear velocity for a rotating object?
4. Give an example of a real-world application of angular velocity.
5. Calculate the angular velocity of a wheel that completes 10 revolutions in 4 seconds.

Understanding angular velocity is important for understanding rotational motion and its applications in various fields of science and engineering.