3. Objectives  Know the definition of torque  Know that torque is directly proportional to the magnitude of the force and the perpendicular distance from the axis of rotation to the line along which the force acts  Know what a lever arm or moment arm is in relation to torque

4. Objectives  Solve problems involving torque  Solve torque problems involving forces applied at an angle other than perpendicular to the moment arm

5. Introductory Video

6. Center of Mass CM

7. Center of Mass CM

8. Center of Gravity CM m1gm1g m2gm2g m system g

9. Center of Gravity Pivot point or fulcrum m1gm1g m2gm2g

10. Center of Gravity Pivot point or fulcrum m1gm1g What’s gonna happen?

11. Torque Pivot point or fulcrum m1gm1g Torque happens!

12. Center of Gravity Pivot point or fulcrum m1gm1g Torque happens!

13. Torque – Case 1 Pivot point or fulcrum m1gm1g m2gm2g

14. Torque – Case 2 Pivot point or fulcrum m1gm1g

15. Torque – Case 3 Pivot point or fulcrum m1gm1gm2gm2g

16. Torque – Case 4 Pivot point or fulcrum m1gm1g m2gm2g

17. Torque  Torque is: 1. The moment of the force about the axis 2. Another name for angular acceleration Pivot point or fulcrum m1gm1g

18. Torque Is  The product of the force times the lever or moment arm. The lever arm is the distance between the force and the axis of rotation or pivot point or fulcrum Pivot point or fulcrum m1gm1g

19. Torque  Since torque is force times distance, it stands to reason that the units will be Newton-meters (N  m) Pivot point or fulcrum m1gm1g

20. Torque  If the blue box is 10kg and 30cm from the pivot point, how much torque is produced and in what direction? Pivot point or fulcrum m1gm1g

21. Torque  If the blue box is 10kg and 30cm from the pivot point, how much torque is produced and in what direction? Pivot point or fulcrum m1gm1g

22. Torque  How much force would have to be applied 10cm from the pivot to balance the box? Pivot point or fulcrum m1gm1g FPFP

23. Torque  What if the force is applied at a 45° angle? Pivot point or fulcrum m1gm1g FPFP

24. Torque  What if the force is applied at a 45° angle?  You still need a vertical force of 294 Nm, so the applied force must be a lot greater. Pivot point or fulcrum m1gm1g FPFP 294 Nm

25. Torque  What if the force is applied at a 45° angle? Pivot point or fulcrum m1gm1g FPFP 294 Nm 45°

27. Summary Review  Do you know the definition of torque  Do you know that torque is directly proportional to the magnitude of the force and the perpendicular distance from the axis of rotation to the line along which the force acts  Do you know what a lever arm or moment arm is in relation to torque

28. Summary Review  Can you solve problems involving torque  Can you solve torque problems involving forces applied at an angle other than perpendicular to the moment arm

30. #29-33 Homework