Question

A child is spinning a rock at the end of a 2-foot rope at the rate of 180 revolutions per minute (rpm). Find the linear speed in feet per minute of the rock when it is released.

Answer 1

Given:

A child is spinning a rock at the end of a 2-foot rope at the rate of 180 revolutions per minute (rpm).

To find:

Linear speed of the child at the periphery of the rock in feet/min.

Calculation:

First of all, we need to convert the unit of angular velocity from rpm to rad/min. We just need to multiply by 2π:

$\therefore \: 180 \: rpm = 180 \times 2\pi = 360\pi \: rad/min$

Now , linear speed can be calculated by multiplying the angular speed with radius of the rock (the periphery at which the child is sitting):

$\therefore \: v = \omega \times r$

$\implies \: v = 360\pi \times 2$

$\implies \: v = 720\pi \: feet/min$

So, linear velocity is 720π feet/min.