Question

A particle starts rotating from rest and its angular displacement is given by theta =t^2/40+t/5.

Answer 1

Answer:

Angular velocity$=\frac{t}{20}+\frac{1}{5}$

Angular acceleration$=\frac{1}{20}$

Explanation:

Concept:

If the angular displacement is $\theta$, then

Angular velocity$=\frac{d\theta}{dt}$

Angular acceleration$=\frac{d^2\theta}{dt^2}$

Given:

$\theta =\frac{t^2}{40}+\frac{t}{5}$

Now,

Angular velocity$=\frac{d\theta}{dt}$

Angular velocity$=\frac{2t}{40}+\frac{1}{5}$

Angular velocity$=\frac{t}{20}+\frac{1}{5}$

Angular acceleration$=\frac{d^2\theta}{dt^2}$

Angular acceleration$=\frac{1}{20}$