You spend some time experimenting with a baseball bat, and eventually you are able to balance the bat on a single finger. A friend notices this, and makes the following claim:
“It looks like the balancing point isn’t in the middle of the bat—it’s a little closer to the thicker end of the bat. That balancing point must be the location where half the bat’s mass is on the left and half the bat’s mass is on the right.”
Calculate the moment of inertia by direct integration of a thin rod of mass \(M\) and length \(L\) about an axis through the rod at \(L/3\text{,}\) as shown below. Check your answer with the parallel-axis theorem.
You have a triangular piece of metal with total mass \(M\text{,}\) base length \(L\text{,}\) and height \(H\text{.}\) You know the mass density is uniform. Find the center of mass of the piece of metal.
A tennis ball can be modeled as a spherical shell with total mass \(M\) concentrated at radius \(R\text{.}\) Calculate the moment of inertia about an axis passing through the center of the tennis ball.
