A thin, rigid disk rotates about its central axis. The angular position of a reference line on the disk as a function of time is described as follows:
• From t=0s to t=2s, θ increases uniformly from 0rad to πrad.
• From t=2s to t=4s, θ remains constant at πrad.
• From t=4s to t=6s, θ increases with time according to θ(t)=π+0.25(t−4)2, where t is in seconds and θ is in radians.
Two insects, A and B, ride on the surface of the disk at fixed radial distances rA=0.10m and rB=0.20m, respectively.
Answer the following questions about the linear motion of each insect.
(1) Part 1: (a) Describe qualitatively how the shape of the linear‐displacement–versus–time graph sA(t) for insect A compares with the given θ(t) description in each of the three time intervals.
(2) Part 2: (b) On the same set of axes, sketch the expected graphs of sA(t) and sB(t) from t=0s to t=6s. Clearly label both curves and all numerical intercepts you can determine.
(3) Part 3: (c) For each insect, identify every time interval during which the magnitude of its tangential acceleration is zero. Justify your answer with reference to the information given in the stimulus.
(4) Part 4: (d) During the final interval (4s≤t≤6s), compare the instantaneous linear speeds of insects A and B. Explain the physical cause of any differences in their speeds.