1. Predict the readings on the scales: ? 1030 20 0 ? 1030 20 0 0.5m 1.0 m M bar = 1.0 kg 1.0 kg

2. Predict the readings on the scales: 1030 20 0 1030 20 0 0.5m 1.0 m M bar = 1.0 kg 1.0 kg 10 N

3. Now predict the readings: ? 1030 20 0 ? 1030 20 0 0.8m 1.0 m M bar = 1.0 kg 1.0 kg a=0

4. Which force is most effective in causing rotation? standard frictionless pond standard meter stick F1F1 F2F2 standard pivot point

5. Now which force is most effective in causing rotation? standard frictionless pond standard meter stick F1F1 F2F2 standard pivot point

6. Definition of torque  rF perp

7. In practice…. Pivot F = 200 N r = 3 m  = r F = (3 m)(200 N) = 600 m - N

8. Useful force method: only the component F perp causes torque. Fixed Pivot Point F r   = r (F sin   F sin  = r F perp

9. Torque A torque is produced when a force is applied with “leverage”. net torque causes angular acceleration Only the perpendicular force contributes to the Torque.

10. Torque net torque causes angular acceleration if the force is applied “off center” If net torque = 0, angular velocity(  ) = constant. Doubling the net torque doubles angular acceleration (  ).

11. Let’s practice: 200 N ? 1030 20 0 1.0 m 200 N pivot

12. Let’s practice: 200 N ? 1030 20 0 1.0 m 400 N pivot 0.5m

13. Linear equilibrium: 150 N 100 N ??? N a = 0 F left = F right

14. Rotational equilibrium 200 N ? 1030 20 0 1.0 m 800 N pivot 0.25m  = 0  1 =  2

15. Let’s solve the problem: ? 1030 20 0 ? 1030 20 0 0.8m 1.0 m M bar = 1.0 kg 1.0 kg a = 0  F net = 0  = 0   net = 0

16. TLTL TRTR 0.8m 10 N 0.5m 10 N Pivot (10 N)(.5 m) + (10 N)(.8 m) = T R (1 m) T R = 13 NT L = 7 N  1 =  2

17. Let’s solve the problem: ? 1030 20 0 ? 1030 20 0 0.6m 1.0 m M bar = 1.0 kg 1.0 kg a = 0  F net = 0  = 0   net = 0