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.
Standard moments of inertia
Torque as a cross product
Rolling down an incline
Rotational form of Newton's second law
Parallel axis theorem
Deriving a moment of inertia
Equilibrium of a leaning ladder
Moment of inertia by integration
Combining translation and rotation
Angular kinematics with calculus
Torque about different axes
Why the axis matters
Short answer 1. Define or explain: Direction of friction in rolling
3 ptsShort answer 2. Define or explain: Torque from a distributed force
3 ptsShort answer 3. Define or explain: Static equilibrium conditions
3 ptsShort answer 4. Define or explain: Rolling without slipping
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.