Answer to Question #78154 in Mechanics | Relativity for Prerana

Question

Define torque and explain its physical
meaning. A merry-go-round of radius 4.0 m
is set rotating clockwise from rest. It attains
an angular speed of 0.10 rad s-1 in 20 s.
What is the torque experienced by a child of
mass 25 kg sitting at the edge of the
merry-go-round ? When will the angular
momentum of this system be constant ?

Answer 1

Torque is the cross product of force and displacement vector.
It is the rotational force which causes the angular displacement.

Here, angular speed = 0.10 rad/sec.
Angular acceleration = 0.1/20 = 0.005 rad/sec2.
Now, moment of inertia = mass x (radius)2
= 25 x 16 [As mass = 25 kg, radius = 4 m]
= 400 kg-m2
Now, the torque = moment of inertia x angular acceleration = 400 x 0.005 = 2 Newton-meter.
When the net torque is zero, the angular momentum of the system will be constant.


Answer: The required torque is 2 N-m. And the angular momentum will be constant when the net torque is zero.