Lesson 39
Angular Momentum and Torque

Name:faculty Section:M2 Start Time:19:53:17 Instructor:pate Course:355

1) Consider the cube (with sides of length a) shown in the figure. The origin of the axes is at the back corner of the cube.

If you spin the cube about any of the axes shown in the figure, with angular speed w, will the angular momentum of the cube be in the same direction as the angular velocity vector? Why or why not?

What would you do if you wanted to actually calculate the angular momentum vector components L1, L2, and L3? That is, what equation would you use and how would you actually do the calculation?





2) Imagine four equal masses glued to the surface of a thin plastic spherical shell of radius R as shown in the figure. The masses are located at opposite ends of mutually perpendicular diameters, and the shell rotates with constant angular velocity w, carrying with it the four equal masses. (Yes -- there would need to be some bearings that would provide whatever torque is required to ensure the uniform rotation.)

If the coordinate system is centered at the center of the sphere and has its axes as shown in the figure, estimate what the moment of inertia tensor would be like.

Will the angular momentum of this system be along the direction of the angular velocity vector? Why or why not?





3) Which of the following is NOT a valid general expression for rotational kinetic energy?








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