Three Dimensional Roation: Problem Solving

1. Three Dimensional Roation: Problem Solving 8.01 W14D2 Today’s Reading Assignment Young and Freedman: 10.7

2. Problem Set 11 Due Thursday Dec 8 9 pm Sunday Tutoring in 26-152 from 1-5 pm Announcements

3. Concept Question: Rotating Rod Consider a massless rod of length I with two point-like objects of mass m at each end, rotating about the vertical z-axis with angular speed ω. There is a sleeve on the axis of rotation. At the moment shown in the figure, two forces are acting on the sleeve. The direction of the change of the angular momentum about the center of mass points along the z-axis. along the line formed by the rod. in the plane of the figure, perpendicular to the line formed by the rod. into the plane of the figure. out of the plane of the figure.

4. Concept Q. Answer: Rotating Rod Answer 4. The torque about the center of mass points into the plane of the figure. Therefore the direction of the change of the angular momentum about the center of mass points into the plane of the figure.

5. Calculate torque about appropriate point P, • Calculate angular momentum about P, • Apply approximation that to decide which contribution to the angular momentum about P is changing in time. Calculate • Apply torque law to determine direction and magnitude of angular precessional velocity • Apply Newton’s Second Law to center of mass motion Problem Solving Strategy

6. Table Problem: Suspended Gyroscope

7. Table Prob. Gyroscope on Rotating Platform

8. Table Problem: Mill Stone

9. Table Problem: Sopwith Camel The Sopwith Camel was a single-engine fighter plane flown by British pilots during WWI (and also by the character Snoopy in the Peanuts comic strip). It was powered by a radial engine, and the entire engine rotated with the propeller. The Camel had an unfortunate property: if the pilot turned to the right the plane Tended to go into dive, while a left turn caused the plane to climb steeply. These tendencies caused inexperienced pilots to crash or stall during takeoff.

10. Table Problem: Sopwith Camel From the perspective of the pilot, who sat behind the engine, did the engine rotate clockwise or counter clockwise? Odd tables: Argue on the basis of torque (and third law pairs). Even tables: Argue on the basis of conservation of angular momentum in the horizontal plane.

13. Concept Question: Stabilizing a Turning Car When making a turn every car has a tendency to roll over because its center of mass is above the plane where the wheels contact the road. Imagine a race car going counter clockwise on a circular track. It could mitigate this effect by mounting a gyroscope on the car. To be effective the angular velocity vector of the gyro should point . 1) ahead 2) behind 3) to the left 4) to the right 5) up 6) down

14. Concept Question: Stabilizing a Turning Car Note that the same orientation of the gyro will stabilize the car when it turns to the right as well. The torque applied to the car by the gyro will change direction, pointing toward the rear of the car instead of the front. But now the result of the curved path is tending to roll the car to the left instead of to the right. The gyro still acts to prevent a roll-over.