A thin, horizontal turntable can rotate without friction about a central vertical…
PHYSICS · Multi-part · CBSE · Physics · System of Particles and Rotational Motion · System of Particles and Rotational Motion
Problem
A thin, horizontal turntable can rotate without friction about a central vertical axis. Its angular acceleration is constant and equal to 1.5rad/s2 in the counter-clockwise direction. A small bug starts at the center of the turntable at t=0 and walks straight outward along a radial line at a constant speed of 0.010m/s relative to the surface of the turntable. Neglect any interaction between the bug and the air.
Investigate the bug’s motion relative to the ground (an inertial frame).
(a) Express the bug’s radial position r(t) measured from the axis as a function of time.
(b) Using your result from part (a), derive an expression for the magnitude of the bug’s tangential acceleration at(t) relative to the ground.
(c) Calculate the numerical value of at at t=4.0s. Provide units with your answer.
(d) Discuss briefly whether the bug’s tangential acceleration would increase, decrease, or stay the same if it walked inward toward the axis instead, still at 0.010m/s. Support your answer with reasoning based on your expression from part (b).