Understanding Angular Velocity in Physics

1. Angular Velocity www.assignmentpoint.com

2. In physics, the angular velocity is defined as the rate of change of angular displacement and is a vector quantity (more precisely, apseudo vector) which specifies the angular speed (rotational speed) of an object and the axis about which the object is rotating. This speed can be measured in the SI unit of angular velocity, radians per second, or in terms of degrees per second, degrees per hour, etc. Angular velocity is usually represented by the symbol omega (ω, rarely Ω). www.assignmentpoint.com

3. The angular velocity is defined as the rate of change of angular displacement and is a vector quantity which specifies the angular speed or rotational speed of an object and the axis about which the object is rotating. The direction of the angular velocity vector is perpendicular to the plane of rotation, in a direction which is usually specified by the right-hand rule. www.assignmentpoint.com

4. Angular Velocity • A particle on a circular path moves through an angular displacement ∆f–iin a time interval ∆t = tf – ti. • In analogy with linear motion, we define: • As the time interval ∆t becomes very small, we arrive at the definition of instantaneous angular velocity. www.assignmentpoint.com

5. Angular Velocity • Angular velocity ω is the rate at which a particle’s angular position is changing. • As shown in the figure, ωcan be positive or negative, and this follows from our definition of . • A particle moves with uniform circular motion if ω is constant. • ω and  are related graphically: www.assignmentpoint.com

6. Angular Velocity in Uniform Circular Motion • When angular velocity ω is constant, this is uniform circular motion. • In this case, as the particle goes around a circle one time, its angular displacement is  2 during one period tT. • The absolute value of the constant angular velocity is related to the period of the motion by: www.assignmentpoint.com

7. Example: At the Roulette Wheel www.assignmentpoint.com

8. Example: At the Roulette Wheel www.assignmentpoint.com