Energy and Momentum of Rotating Systems unit test
A test on this unit alone, marked as a percentage and a letter grade — for the test your class is actually sitting, rather than for May. Answer everything, then submit once: seeing the answer to question 3 before attempting question 4 makes the final percentage meaningless.
Why kinetic energy is not conserved when I changes
Particle striking a pivoted rod
Rolling race is independent of mass and radius
Energy change when I changes
Rotational work and power
Conservation of angular momentum
Orbital angular momentum is conserved but energy determines the shape
Gyroscopic precession
Angular momentum in an elliptical orbit
When angular momentum is conserved
Choosing the point for angular momentum
Rotational kinetic energy as the analogue of ½mv²
Short answer 1. Define or explain: Angular impulse
3 ptsShort answer 2. Define or explain: Precession qualitatively
3 ptsShort answer 3. Define or explain: Work–energy theorem for rotation
3 ptsShort answer 4. Define or explain: Rotational kinetic energy
3 ptsFree response
8 ptsA solid sphere and a hollow spherical shell have the same mass M and the same radius R. Both are released from rest at the same height on an incline and roll without slipping to the bottom.
A. Indicate whether the solid sphere reaches the bottom of the incline before, after, or at the same time as the hollow shell. Justify your answer using qualitative reasoning beyond referencing equations.
B. Derive an expression for the translational speed of a rolling object of mass M, radius R and rotational inertia I = βMR² at the bottom of an incline of height h, in terms of β, h and physical constants.
C. Justify how your derived expression in part B is or is not consistent with your comparison in part A. (For a solid sphere β = 2/5; for a thin spherical shell β = 2/3.)