A teacher asks students to discuss motion on a rotating merry-go-round that spins at a constant angular velocity. Three student statements are written on the board:
• Statement I: “All riders complete one revolution in the same amount of time, so everyone has the same linear speed.”
• Statement II: “Because the merry-go-round turns uniformly, riders at different radii have identical tangential accelerations.”
• Statement III: “Riders farther from the center travel a greater distance during each revolution than riders closer in.”
a. Evaluate the correctness of Statement I. Provide a clear justification for your evaluation.
b. Evaluate the correctness of Statement II. Provide a clear justification for your evaluation.
c. Evaluate the correctness of Statement III. Provide a clear justification for your evaluation.
d. Based on your evaluations, summarize how the motion of riders depends on their radial position when the merry-go-round turns at constant angular velocity.