Question

Two children are riding a marry-go-round. Child (P) rides on the outside rim of the merry-go-round, while child (L) rides on the inside rim of the merry-go-round. A at the end of the ride, identify the correct statements about children?
(A) Child (P) had the largest angular displacement.
(B) Child (L) had the largest tangential displacement.
(C) Child (P) had the largest tangential velocity.
(D) Child (L) had the largest angular velocity.

Answer 1

Hint: To answer this question we should know the difference between angular displacement, tangential displacement, tangential velocity and angular velocity.

Complete step by step answer
Displacement: The change of position. The distance travelled by an object
Displacement = Final distance travelled – Initial distance travelled
Angular displacement: Rate of Change in position of angle i.e. when an angle change its position from one to another
Angular displacement= Initial angle - Final angle
Tangential displacement: It is the rate of change in position of an object along a circular path.
Tangential displacement= Final distance travelled along circular path – Initial distance travelled along circular path
Velocity: The velocity of an object is defined as the change of rate of its position with respect to time and direction. The rate of change of displacement with respect to time
Velocity = Displacement/Time taken.
$v = \dfrac{s}{t}$
Where,
$v$ is velocity
$s$ is displacement
$t$ is time
Angular velocity : The rate of change of an angle with respect to time i.e. when an angle changes from one angle to other angle with respect to time rate of change of angular displacement with respect to is known as angular velocity
Angular velocity= Angular displacement/Time taken.
$\omega = \dfrac{{d\theta }}{{dt}}$
$\omega $ is the angular velocity
$\theta $ is the angle
$t$ is time
Tangential velocity: The rate of change of position of a body along the circular path. When a body moves in a circular path the body’s velocity is directed tangentially at any instant. This is known as tangential velocity.
Tangential velocity= Tangential displacement/Time taken.
${V_r} = r \times \omega $
${V_r}$ is the Tangential velocity
$r$ is the radius of the circle
$\omega $ is the angular velocity
Given,
The merry-go-round is circular in shape. The children inside and outside the merry-go-round covers equal angles in equal time. So their angular displacement and angular velocity will be equal. The displacement in the circular path will also be equal for both the children.
At last if we take tangential velocity
$ \Rightarrow {V_r} = r \times \omega $
It is the product of angular velocity and the radius of the circle
The angular velocity will be equal for both the children but the radius will be large for the child outside the merry go round.
So the child (P) who is outside will have the largest tangential velocity.

Hence the correct answer is option (C) Child (P) had the largest tangential velocity.

Note: The Tangential velocity depends on the radius of the circular path it acts along, whether angular velocity does not depend on the radius of the path.