find the kinetic energy

Question

A point-mass of 20 grams at the end of a massless 90 centimeter long string is rotated at a rate of 5 revolutions per second. Find the kinetic energy of the point mass in ergs.

Answer 1

Hi Lily!

The rotational kinetic energy formula is 1/2*L*ω^2 where L is the moment of inertia of our mass and ω is the rotational velocity in radians per second.

First, we need to convert our rotational velocity. Since there are 2π radians in one revolution, we have a rotational velocity ω of 10π.

Our moment of inertia in this case of a point mass is simply L = m*r^2, so (first converting to Kg and m) 0.02*0.09^2 = 0.000162 Kg*m^2

Plugging into our formula,

1/2*0.000162*(10π)^2 = 0.079944 J

Since they want our answer in ergs, which is just 10^(-7) J, our answer is 7.9944*10^5 ergs.

The moment of inertia can be tricky to determine in most cases because it changes depending on the size, shape, and position of the mass that is rotating. Technically it requires some integration that can be as simple or complex as the problem wants, but in your case for highschool physics there are a bunch of useful tables on google that will provide you with the moment of inertia of many common objects your teacher will ask you about. In this problem we had a point mass, but a different example would be a sphere rotating around its center where its moment of inertia is 2/5m*r^2.

Also, when in doubt, convert everything into radians, Kg, and meters

Hope this helps!