Torque and Rotational Dynamics 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.
Slipping vs rolling
Parallel axis theorem
Direction of friction in rolling
Angular kinematics with calculus
Torque about different axes
Torque as a cross product
Deriving a moment of inertia
Rolling without slipping
Why the axis matters
Rotational form of Newton's second law
Torque from a distributed force
Combining translation and rotation
Short answer 1. Define or explain: Moment of inertia by integration
3 ptsShort answer 2. Define or explain: Standard moments of inertia
3 ptsShort answer 3. Define or explain: Equilibrium of a leaning ladder
3 ptsShort answer 4. Define or explain: Rolling down an incline
3 ptsFree response
10 ptsA light string is wrapped around a uniform solid disk of mass M = 3.0 kg and radius R = 0.25 m that rotates on a frictionless horizontal axle through its center. A block of mass m = 1.0 kg hangs from the free end of the string, which does not slip on the disk. Take g = 9.8 m/s².
Using I = ∫r²dm, derive the rotational inertia of the disk about its center and evaluate it.
Write Newton’s second law for the block and the rotational form for the disk, and determine the acceleration of the block.
Determine the tension in the string.
Use energy methods to determine the angular speed of the disk after the block has descended 0.80 m, and verify your answer with kinematics.
Explain why the tension is not equal to the block’s weight, and state what the tension approaches if the disk’s mass is made very large.