A rotating playground platform is observed from above. Its angular position θ (measured in radians, where counter-clockwise is taken as positive) is recorded every 1.0s for a total of 10s. The results are shown below.
Time t (s): 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0
Angular position θ (rad): 0.0 0.50 1.20 2.00 2.90 3.50 3.80 3.90 3.85 3.70 3.30
Assume the platform is a rigid system rotating about a fixed vertical axis through its center.
(a) Describe, without calculation, how the direction of rotation changes (if at all) during the 10s interval. Cite specific features of the data that support your description.
(b) Explain whether the average angular velocity over the entire 10s interval is positive, negative, or zero. Justify your reasoning by referring to the numerical values in the table.
(c) At t=2.0s the platform’s instantaneous angular velocity is the slope of the θ–versus–t curve at that instant. Compare qualitatively this instantaneous angular velocity to the average angular velocity you discussed in part (b), and explain why the two values might differ.