Creative Commons License Copyright © Michael Richmond. This work is licensed under a Creative Commons License.

Some examples of simple moments of inertia

Let's try an easy calculation. Suppose we make a triangle out of three balls, connected by massless rods. Each ball has mass m = 3 kg, and they are arranged in an equilateral triangle with sides of length L = 10 m. We spin the triangle around the spot marked "X", which is one of the balls. 



  Q:  What is the moment of inertia of this triangle, spinning
           around the ball marked "X"?

My answer.

Okay, let's try a harder one. Suppose that we locate the center of mass of the triangle -- I've marked it with the "X" in the figure below.

  1. What is the distance from each ball to the center of rotation now?
  2. What's the moment of inertia of the triangle spun around this point?
  3. What is the KE of the structure if it spins at 12 degrees per second?
  4. How many RPMs are required to give the structure a kinetic energy of 1000 Joules?

My answers.

Creative Commons License Copyright © Michael Richmond. This work is licensed under a Creative Commons License.