PHYS 211 Lecture 16: Unit 16 Parallel Axis Theorem and Torque.pdf
Document Summary
Prove theorem relating moments of inertia about parallel axis. Develop the equation that determines the dynamics for rotational motion. Find the rotational analog of mass that is the moment of inertia. For a solid object, the only motion relative to the center of mass is rotation. The moment of inertia about a chosen axis if the moment of inertia through a parallel axis that goes through center of mass is known. So the center of mass rotating about the axis plus the rod itself rotating at the same rate. Moment of inertia about dumbbell is sum of the moment of inertia around the rod and both bells. Inertia sphere about given axis = 2/5mr^2 + m(l/2)^2. If dw/dt > 0, then alpha points in same direction of omega. If dw/dt < 0, then alpha points in opposite direction of omega. Does not depend on choice of coordinate system. Everything is a property of the object itself.
