# A carousel is rotating at such a rate that a horse located 8.0 m from the axis of rotation moves...

## Question:

A carousel is rotating at such a rate that a horse located {eq}8.0 \, \mathrm{m} {/eq} from the axis of rotation moves at a speed of {eq}6.0 \, \mathrm{m/s} {/eq}.

(a) What is the period of the rotation of the horse?

(b) What is the centripetal acceleration of the horse?

(c) What is the speed of a second horse, {eq}4.0 \, \mathrm{m} {/eq} from the axis?

(d) What is the centripetal force acting on the second horse if it has a mass of {eq}150 \, \mathrm{kg} {/eq}?

## Centripetal Acceleration:

Consider an object moving around the edge of a circle at a constant speed. In order to follow this path, the direction of the object's velocity must constantly change. This means that the object is constantly accelerating. This is called the centripetal acceleration, {eq}a_c {/eq}.

Centripetal acceleration is given by the formula:

{eq}a_c = \dfrac{v^2}{r} {/eq}

Here {eq}v {/eq} is the object's speed and {eq}r {/eq} is the radius of the circular path.

(a) The period {eq}T {/eq} is the amount of time it takes for the horse to complete one full revolution. We can express this as the distance the...

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