1. Rotational Mechanics

2. Torque When you want an object to turn or rotate, you apply a torque. Torques produce rotation.

3. Torque Torque is produced when a force is applied with “leverage”. Ex) If you want to pull a nail from a piece of wood, the longer the handle of the hammer, the easier of the task.

4. Torque A door knob is placed far away from the turning axis of the hinges to provide more leverage. Direction of the applied force is also important for torque. – Example, you would never pull/push the doorknob side to side to open the door, but instead apply the force perpendicular to the door.

5. Mathematics of torque Torque = perpendicular force * lever arm Conceptually – The same torque can be produced by a large force with a short lever arm, or a small force with a long lever arm The second is better for tool application. – Greater torques are produced when both the force and lever are large.

6. Seesaws Even when weights are not equal, a seesaw can be balanced. Weight alone does not produce rotation, torque does. How can you balance a seesaw with a large kid on one side and a small kid on the other?

7. Balanced Torques Another application of balanced torques is scale balances. The sliding weights are adjusted so that the arm remains horizontal.

8. Activity Hang a meter stick so that it is balanced. Hang a 20g mass from the 10cm mark on the meter stick. Where should a 100g mass be placed to balance the meter stick?

9. Recall An object will topple if its center of gravity is not above a support base. The reason for this toppling is that you now have applied a torque around the center of gravity.

10. What determines how a football flies? First a force is required to launch the projectile. If all the force is through the CG, then the football will move as a whole. If the force is directed “off-center”, then the CG will be launched and also the object will rotate about its CG

11. Frisbee To get a Frisbee to fly, you need to apply a force so that the CG will move. To get a Frisbee to rotate, a force must applied off axis to give it a torque.

12. Rotational Inertia An object rotating about an axis tends to keep rotating about that axis. There is a resistance of an object to change its rotational motion.

13. Connection to forces Just as it takes a force to change an object’s linear motion, it takes a torque to change an object’s rotational motion. Rotational motion depends on the mass of the object, but also the distribution of the mass. The greater the distance of the bulk of the mass from the turning axis, the more rotational inertia.

14. Choking up in baseball A long bat is harder to bring up to speed because the bulk of the mass is farther from the handle (axis of rotation) than a bat you “choke up” on. Long-legged animals normally run with a slower gait for the same reason.

15. Pendulums Two pendulums, with the same mass are swinging. One has a longer string holding it than the other. Which has a faster swing?

16. Tightrope walker Why does the tightrope walker have a long pole to help him balance? It is increases their rotational inertia and makes him resist rotation over the edge of the rope.

17. Demonstration Stand up and stand to the side of the lab table. Swing one leg back and forth with a straight leg. Now bend the leg and swing back and forth. Which is easier? Why? Connect to running.

18. Demonstration Flipping your pencil back and forth. Hold it in near the end and try to flip the pencil back and forth. Now hold it in the middle.

19. Rotational Inertia of a Human There are three principle axes of rotation for a human. Each has a different rotational inertia. Which way is it easiest to rotate? (in the absence of gravity) How can you increase the rotational inertia of the longitudinal axis?

20. Flipping Why is it better to “tuck” if you want to get more flips in before hitting the water if you are a diver?

21. Angular Momentum An object that is rotating tends to continue to rotate unless acted upon by a torque. The inertia of rotation is known as angular momentum. Angular momentum = rotational inertia * rotational velocity

22. Video Bicycle wheel gyroscope

23. Bicycles An object or system of objects will maintain its angular momentum unless acted upon by a torque. When the wheels are at rest, we fall over. When the wheels are moving, they have angular momentum, and a greater torque is required to change the direction of the angular momentum.

24. Conservation of angular momentum If no unbalanced external torque acts on a rotating system, the angular momentum of that system is constant. Explain the following example demonstration…

25. Figure skater spinning