1. Angular Variables

2. We use degrees to measure position around the circle. There are 2p radians in the circle. This matches 360° The distance around a circle is s = rq, where q is in radians. Measuring a Circle Dq q r The angular displacement is Dq

3. Angular Velocity • For circular motion, only the time rate of change of the angle matters. • The time rate of change of the angle is called the angular velocity. • Symbol (w) • Units (rad/s or 1/s = s-1)

4. Velocity and Angular Velocity • Velocity has an angular equivalent. • Linear velocity (v) • Angular velocity (w) • They are related, since the displacement is related to the angle.

5. Frequency is measured in cycles per second. There is one cycle per period. Frequency is the inverse of the period, f =1/T. Angular velocity is measured in radians per second. There are 2p radians per period. Angular velocity, w = 2p/T. Angular velocity, w = 2pf. Cycles or Radians

6. Angular Acceleration • In uniform circular motion there is a constant radial acceleration. • ar = v2 / r = rw2 • If the angular velocity changes there is acceleration tangent to the circle as well as radially. The angular acceleration is a

7. Uniform or Nonuniform • Centripetal acceleration is constant for uniform circular motion. • It changes for nonuniform circular motion. • The magnitude increases or decreases. • There is a tangential acceleration. • Net vector is not antiparallel to radius.

8. Kinematic equations with constant linear acceleration were defined. vav = ½ (v0 + v) v = v0 + at x = x0 + v0t + ½at2 v2 = v02 + 2a(x - x0 ) Kinematic equations with constant angular acceleration are similar. wav = ½ (w0 + w) w = w0 + at q = q0 + w0t + ½at2 w2 = w02 + 2a(q - q0 ) Rotational Motion next