By Team Aakash Byju's | 19th November 2022

How to Find the Maximum Angular Velocity in a Circular Motion?

A weightless thread can withstand tension up to 30 N. A stone of mass 0.5 kg is tied to it and is revolved in a circular path of radius 2 m in a vertical plane. If g = 10 ms, then

(Angular velocity)

-2

maximum

=

√30 rad/s

A.

(Angular velocity)

maximum

=

√60 rad/s

B.

(Angular velocity)

maximum

=

5 rad/s

C.

maximum

=

6 rad/s

D.

(Angular velocity)

Detailed Explanation

The correct answer is   option C. 5 rad/s.

Arrow

For the given situation, when the stone is at the lowest position of the vertical motion, the tension is maximum.

W

T

r

Mass of the object and gravity

 Radius

Angular  velocity

Tension

mg

W

T

r

Mass of the object and gravity

 Radius

Angular  velocity

Tension

mg

Using the equation of circular motion we can write:

mr

( w      )

max

2

=

T

max

-mg

Where, w       is the maximum angular velocity.

max

W

T

r

Mass of the object and gravity

 Radius

Angular  velocity

Tension

mg

T       = 30 N, m = 0.5 kg,   r = 2 m, g = 10 ms

max

-2

(0.5)(2) (w      )  = 30 − (0.5 × 10)

max

2

Given,

W

T

r

Mass of the object and gravity

 Radius

Angular  velocity

Tension

mg

=>(w       )  =30 − 5 = 25

max

=>w       = 5 radians per                      second.

max

2