A physicist verbally describes the following straight-line graph of angular velocity versus time for a rigid disk. The graph is a straight line that begins at point (t=0,ω=+10rads−1) and ends at point (t=3.0s,ω=−5.0rads−1). Counter-clockwise rotation is considered positive throughout the motion.
Assume the angular acceleration is constant over the interval.
a. Part 1: (a) Derive the numerical value (including sign) of the disk’s constant angular acceleration.
b. Part 2: (b) Determine the exact clock time at which the disk reverses its direction of rotation. Show all reasoning.
c. Part 3: (c) Calculate the net angular displacement of the disk from t=0 to t=3.0s. Express your answer in radians and indicate its sign.
d. Part 4: (d) Explain why the sign of your answer in part (c) is consistent with the area-under-the-curve interpretation of the ω-t graph.