Activity 13.5.1. Three Spheres.
Adjacent spheres below are separated from their nearest neighbor by a distance \(L\text{.}\) Find the center of mass of the system of three spheres.
Section 13.5 Moment of Inertia Exercises
Activity 13.5.2. The Hammer.
You want to balance the hammer vertically with the tip of your finger. Which side of the hammer will be easier to balance?
Activity 13.5.3. The Baseball Bat I.
A futuristic model for a baseball bat of mass \(M\) is the triangle shown below. The bat has length \(L\) and its widest width is \(W\text{.}\) You want to find the bat’s center of mass.
(a)
Draw a picture. What origin do you want to choose?
(b)
Chop: How would you chop the baseball bat into small pieces? Draw a diagram showing the small pieces and label \(dm\text{,}\) \(dA\text{,}\) and \(r\text{.}\) Find the mass of one of the small pieces you drew.
(c)
Multiply: Using the results from the previous steps, multiply the components together to get your infinitesimal \(d\vec{r}_{cm}\text{.}\)
(d)
Add: Compute the integral for the center of mass.
Activity 13.5.4. The Baseball Bat II.
Suppose you want to hold the bat from the previous activity horizontally with one hand at the left end. Sketch an extended free-body diagram for the bat that would allow this.
Activity 13.5.5. The Baseball Bat III.
Use the simplified model above for a baseball bat to find the moment of inertia about a vertical rotational axis through the left end of the bat.
Activity 13.5.6. The Plank.
The instructor sits on the chair in the middle of the room. They will push off the floor with the same force, but they will hold the plank in two different orientations: vertically and horizontally. Which orientation will result in the instructor spinning faster?
