Day 35: R^2 Dependance of Rotational Inertia

Today we were playing around with the Inertia Wands from Pasco. The blue and red wands have identical massess, but different mass distributions. The red wand has 2 masses at its center, while the blue wand has 1 mass on each end. When the wands are held at their centers, they are equally easy to translate by moving your arms forwards and backwards, but the blue wand is much more difficult to rotate by twisting your wrists.

But then a student asked, “What happens if you hold the wands by the end? Which is more difficult to rotate?” So we tried to reason it out and make a prediction first. If you hold the red wand at the end, then there is a mass of 2M located a distance of L/2 from your hand. If you hold the blue wand at the end, then there is a mass of M located a distance L from your hand. They quickly assumed both wands would be equally easy/difficult to move.

But when we tested it out (as seen in the video), the blue wand was still more difficult to move. It was a nice introduction/motivation for the R² dependence of rotational inertia.