A circular turntable spins horizontally about its central axis with a constant…
PHYSICS · Multi-part · CBSE · Physics · System of Particles and Rotational Motion · System of Particles and Rotational Motion
Problem
A circular turntable spins horizontally about its central axis with a constant angular velocity. Two small insects, Ant P and Ant Q, cling to the surface. Ant P is located at a radial distance of 4.0 cm from the axis, while Ant Q is located at a radial distance of 12 cm from the axis. Assume the insects do not slip with respect to the surface.
(1) Describe the relationship between the linear distance each ant travels during any fixed angular displacement of the turntable. Your answer should clearly refer to the radial positions of the ants.
(2) Explain which ant has the greater linear speed. Support your answer with reasoning that refers to the quantities that are the same for both ants and to the quantities that differ.
(3) During the start-up phase the turntable experiences a constant angular acceleration. Compare the tangential (linear) accelerations of the two ants during this phase and explain the physical basis for any difference.
(4) Suppose Ant Q suddenly walks directly toward the center until it reaches the position originally occupied by Ant P, while the turntable’s angular velocity remains unchanged. Qualitatively discuss how Ant Q’s linear speed changes during this inward walk and identify the underlying reason.