An amusement-park ride consists of a large circular platform that rotates in a…
PHYSICS · Multi-part · CBSE · Physics · System of Particles and Rotational Motion · System of Particles and Rotational Motion
Problem
An amusement-park ride consists of a large circular platform that rotates in a horizontal plane. Riders may stand at various distances from the center. The platform’s motion during one operating cycle is described below:
• Acceleration phase: From rest, the platform’s angular speed increases uniformly to 2.0 rad/s in 5.0 s.
• Cruise phase: The angular speed remains constant at 2.0 rad/s for the next 10.0 s.
• Braking phase: The platform then comes to rest with uniform angular deceleration in 3.0 s.
Rider X stands at radius 1.5 m, and rider Y stands at radius 3.0 m.
(a) Determine the magnitude of the platform’s angular acceleration during the acceleration phase and the angular deceleration during the braking phase.
(b) For each rider, calculate the maximum tangential acceleration experienced at any time during the entire operating cycle.
(c) Compute the total linear distance traveled by each rider during the cruise phase only.
(d) Taking the entire 18 s operating cycle into account, which rider travels the greater total linear distance? Quantitatively support your answer.
(e) Identify every time interval during which rider X’s tangential acceleration is zero. Explain how this conclusion follows from the ride’s operating description.