Question

A boy starts to move in a circular path of radius 1 m in the direction ABCDA with constant speed.When boy reaches at point C starting from point A, what is the angular velocity?​

Answer 1

Answer:

Answer is in the attachment

Answer 2

Given:

A boy rotates in a circular path.

Radius = 1 m

To find:

Angular velocity

Solution:

Boy is moving in a circular path in direction ABCDA. He starts at point A and reaches to point C after half rotation via path ABC.

or it covered half circle.

So, distance covered by the boy, d = πr

here, d = distance

          r = radius

now, time taken will be calculated as-

             $time taken = \frac{distance}{speed}$

                     $t = \frac{d}{v}$

here, t = time taken

        d = distance

        v = speed

now,  displacement of a boy for PQ, s = 2r

Formula of angular velocity used is -

                 $v_{ang} = \frac{s}{t}$

here,  $v_{ang}$ = angular velocity

           s = displacement

           t = time taken

by putting all the values, we get

         $v_{ang} = \frac{2r}{\frac{\pi r}{v} }$

         $v_{ang} = \frac{2}{\pi } v$

Therefore, angular velocity is $\frac{2}{\pi } v$.