Question

A carousel at the local carnival rotates once every 45 seconds. (a) What is the linear speed of an outer horse on the carousel, which is 2.75 m from the axis of rotation? (b) What is the linear speed of an inner horse that is 1.75 m from the axis of rotation?

Answer 1

Concepts and reason

The concepts used to solve this problem are linear velocity and angular velocity.

First, use the radius and time period to obtain the linear velocity of the outer horse from the axis of .

Finally, use the radius and angular velocity, to obtain the linear velocity of the inner horse from the axis of .

Fundamentals

The linear velocity is given by the following expression:

$v=ro $

Here, is the radius and is the angular velocity.

The angular velocity is given by the following expression:

Here, is the frequency.

The frequency is given by the following expression:

Here, is the time period.

(a)

The angular velocity is given by the following expression:

The frequency is given by the following expression:

Substitute for .

$=0 $

The linear velocity is given by the following expression:

$v=ro $

Substitute for .

Substitute for and for .

(b)

The linear velocity is given by the following expression:

Substitute for and for .

Ans: Part a

The linear velocity of the outer horse is .

Part b

The linear velocity of the outer horse is .