A circular platform is free to rotate about a central vertical axis

PHYSICS · Multi-part · AP · Physics 1: Algebra-based · Torque and Rotational Dynamics · Torque and Rotational Dynamics

Problem

A circular platform is free to rotate about a central vertical axis. Counter-clockwise rotation is defined as the positive direction. At

t=0

the platform has an angular velocity of

+4.0\,\text{rad}\,\text{s}^{-1}

. A motor then applies a constant angular acceleration of

-1.5\,\text{rad}\,\text{s}^{-2}

for the next

3.0\,\text{s}

. After the motor turns off, no external torques act on the platform. (a) Calculate the angular velocity of the platform at

t = 3.0\,\text{s}

. (b) Determine the angular displacement of the platform (in radians) during the

3.0\,\text{s}

interval. (c) Indicate the direction in which the platform is rotating at

t = 3.0\,\text{s}

and briefly justify your answer using the sign of the angular velocity. (d) How many complete revolutions does the platform make during the

3.0\,\text{s}

interval? Express your answer to the nearest

0.01

revolution.