A Ferris wheel with radius starts from rest and speeds up with a uniform angular…
PHYSICS · Multi-part · AP · Physics 1: Algebra-based · Torque and Rotational Dynamics · Torque and Rotational Dynamics
Problem
A Ferris wheel with radius 12m starts from rest and speeds up with a uniform angular acceleration for several complete revolutions. Two friends sit in separate cars: Rider A is located at the rim of the wheel, while Rider B sits in a car attached to a rigid spoke exactly halfway between the center and the rim.
Throughout the interval in which the wheel is speeding up, both riders share the same angular motion, but their linear experiences differ. Answer the following questions qualitatively and quantitatively, justifying all reasoning without merely quoting formulas.
(a) During the time the wheel is accelerating, compare the magnitudes of the tangential (linear) accelerations of Rider A and Rider B. State which is larger, and justify your answer in terms of how the relevant physical quantities depend on radial position.
(b) At the instant the wheel’s angular speed reaches 0.60rads−1, compare the linear speeds of Riders A and B. Express the ratio vBvA and explain the reasoning that leads to this ratio.
(c) The wheel subsequently completes exactly three full revolutions while it continues to speed up. By what factor is the linear distance traveled by Rider A larger than the distance traveled by Rider B during those three revolutions? Show how you arrive at your result.
(d) Describe how a graph of linear speed versus time would differ for the two riders over the accelerating interval. Identify at least two specific graphical features and connect each to the underlying physics.