A flywheel, starting from rest, has its angular velocity varying with time as…

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

Problem

A flywheel, starting from rest, has its angular velocity varying with time as follows: 0 ≤ t ≤ 3 s:

\omega = 4t

(rad s

^{-1}

) 3 s < t ≤ 6 s:

\omega = 12

(rad s

^{-1}

) 6 s < t ≤ 9 s:

\omega = 12 - 2(t-6)

(rad s

^{-1}

) (i) Calculate the total angular displacement from

t = 0

t = 9\,\text{s}

. (ii) Find the instantaneous angular acceleration at

t = 1\,\text{s}

and at

t = 7\,\text{s}