Physics

Problem

Answer the following questions related to the concept of angular velocity. a. (i) Define average angular velocity and instantaneous angular velocity. b. (ii) Explain, using the idea of a vanishingly small time interval, how the expression for instantaneous angular velocity is obtained from the definition of average angular velocity. c. (iii) A wheel has its angular displacement varying with time according to

\theta = 5t - 2t^{2}

, where

\theta

is in radians and

t

in seconds. Calculate the average angular velocity of the wheel between

t = 0\,\text{s}

and

t = 2\,\text{s}

. d. (iv) Determine the instantaneous angular velocity at

t = 1\,\text{s}

for the same wheel and compare its magnitude with the average value obtained in part (iii).

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