Question

A child has a toy tied to the end of a string and whirls the toy at constant speed in a horizontal circular path of radius R. The toy completes each revolution of its motion in a time period T. What is the magnitude of the acceleration of the toy?

Answer 1

The magnitude of the acceleration is $\frac{4\pi^2 R}{T^2}$

Explanation:

The centripetal acceleration of an object in circular motion is given by the equation:

$a=\frac{v^2}{r}$

where

v is the tangential speed of the object

r is the radius of the circle

The toy in this problem moves along an orbit of radius

r = R

while its period of revolution is T; so, the speed of the toy is the ratio between the circumference and the period:

$v=\frac{2\pi R}{T}$

And substituting into the first equation, we find an expression for the acceleration:

$a=\frac{(\frac{2\pi R}{T})^2}{R}=\frac{4\pi^2 R}{T^2}$

Learn more about circular motion:

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