The angular position (in radians) of a rotating rigid body is given by = 3t^ 3 - 2t^ 2 + t

PHYSICS · Multi-part · A Level · Physics · Engineering physics · Engineering physics

Problem

The angular position

\theta

(in radians) of a rotating rigid body is given by

\theta = 3t^{3} - 2t^{2} + t,

where

t

is in seconds. Use this information to answer the following. (i) Calculate the average angular velocity during the interval from

t = 1\,\text{s}

t = 3\,\text{s}

. (ii) Find the instantaneous angular velocity at

t = 2\,\text{s}

. (iii) Determine the instantaneous angular acceleration at

t = 2\,\text{s}

and state whether the body is speeding up or slowing down at that instant, giving a brief reason.