Rotation

1. Rotation Another Kind of Motion

2. Rotational Motion • Applies to rigid bodies • Also to liquids and gases • All points move in circles about a line called axis of rotation

3. Angular Quantities • Angle q = l/r • In radians • 2pr = 360 deg • 1 radian = 57.3 deg • Angular velocity(average) = w = Dq/Dt (omega) l q r

4. More Angular Quantites • Angular acceleration(average) a = Dw/Dt • Linear velocity v = rw • Frequency of rotation f = w/2p • Units: Hertz = rev/sec • Period T = 1/f

5. Torque • Produces rotation • The rotational analog of force • Depends on direction and where applied • Equals force times lever arm times sine of angle between them t = rFsinq • Unit is meter Newton • Lever arm is perpendicular distance of axis of rotation to line of action of force

6. Torque t = rFsinq Lever arm r Axis of rotation q F

7. How to get the most torque • What angle gives the most torque? • Where should you hold the wrench?

8. Balanced Torques • Net torque produces acceleration • When torques are balanced we have rotational equilibrium • Torques act to rotate a system clockwise or counterclockwise

9. Example • A meter stick rests on a pivot at the center. A 1.0 Newton weight is attached at the 20cm mark. Where must a 2.0 Newton weight be hung on the other side of the string to balance it? (hint: draw it) • Ans. at 65 cm, 15 cm from pivot or fulcrum

10. Angular Momentum • Analog of linear momentum mv • L = Iw (like mv in linear motion) • I is rotational inertia or moment of inertia • I = mr2 for a particle • L = mr2w for single particle (=mvr) • Angular momentum is conserved

11. How does skater speed rotation? • L = Iw = constant