1. Torque & Center of Gravity

2. What is wrong with this door?

3. Turning force = torque Some everyday torques:

4. A torque is produced when a force is applied with leverage.
A doorknob is placed far away from the turning axis at its hinges to provide more leverage when you push or pull.
The longer the handle of the hammer, the greater the leverage, and the easier the task.

5. Torque = Force┴ x lever arm
τ = F┴ x l
When the force is perpendicular, the distance from the axis to the point of contact is called the lever arm
If the force is not at a right angle to the lever arm, then only the perpendicular component of the force F┴ will contribute to the torque.

6. Harry finds it very difficult to muster enough torque to twist a stubborn bolt with his wrench. He wants to increase the torque, so ties a rope to the wrench handle. Will he now have more success twisting the bolt?

7. Suppose your car has a flat tire
Suppose your car has a flat tire. You get out your tools and find a lug wrench to remove the nuts off the bolt studs. You find it impossible to turn the nuts. Your friend suggests ways you might produce enough torque to turn them. What three ways might your friend suggest?

8. Rank the torques on the door from least to greatest.

9. Balanced Torques

10. The distance they sit from the fulcrum is just as important as their weight.

11. Another example

12. Balance is achieved if the torque that tends to produce a clockwise rotation equals the torque that produces a counter clockwise rotation.

13. “Walk the plank” and torque Do you remember our first lab?

14. Torque and center of gravity
An object may behave as if all of its weight is concentrated at one point: “center of gravity”

15. When an object is thrown through the air, its center of gravity follows a smooth parabolic path, even if if the object spins or wobbles.

16. The center of gravity of an object is the point located at the center of an object’s weight distribution.
For a symmetrical object, the CG is at the geometrical center.
For an irregularly shaped object, the CG is closer to the heavier end.
Objects not made of the same material throughout may have the center of gravity quite far from the geometrical center.

17. An object will topple if its center of gravity lies outside its base.

18. Center of gravity above support.

19. Toppling will happen when CG is outside support.

21. How far can you lean over?

22. When you bend over, your center of gravity changes.

23. Why does a pregnant woman get back pains?

24. An object is in stable equilibrium when any displacement raises its CG.

25. An object that is balanced so that any displacement raises its center of gravity is in stable equilibrium.

26. An object balances so that any displacement lowers its center of gravity is in unstable equilibrium.

27. An object is in neutral equilibrium if its CG is neither raised nor lowered with displacement.

28. Locating center of gravity

29. Center of gravity and center of mass vary if the objects are large enough.
Center of gravity for the Sears tower in Chicago is about 1mm below center of mass.