A disc rotates about a fixed axis with the following time–dependence of its angular…

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

Problem

A disc rotates about a fixed axis with the following time–dependence of its angular velocity

\omega

: •

\omega = 4\,\text{rad\,s}^{-1}

for

0 \le t < 2\,\text{s}

, •

\omega

then decreases uniformly to

-2\,\text{rad\,s}^{-1}

t = 6\,\text{s}

(negative sign denotes reversal of sense). Answer the questions below. (i) Calculate the angular displacement of the disc in the time interval

0 \le t \le 6\,\text{s}

. (ii) Determine the average angular velocity for the entire

6\,\text{s}

interval. (iii) At what time between

0

and

6\,\text{s}

is the instantaneous angular velocity equal to the average value obtained in part (ii)?