A*R*C*S 13.7.1. Center of Mass.
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.
Section 13.7 Practice - Moments of Inertia
Subsection Explanation Practice
Subsection A*R*C*S Practice
A*R*C*S 13.7.2. Moment of Inertia of a Tennis Ball.
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.
A*R*C*S 13.7.3. The Cheese Slice.
You have a one-dimensional slice of cheese with total mass \(M\) and total length \(L\text{.}\) You know the linear mass density is \(\lambda(x) = k \sqrt{x}\text{.}\) Find the constant of proportionality \(k\) (including its units) and the center of mass of the slice of cheese.
Tip.
For your representation (part 1c), sketch a graph of the mass density vs. x. This graph might also prove useful for your sensemaking at the end!
Subsection Numerical Practice
Calculation 13.7.4. Moment of Inertia.
Which of the following statements concerning the moment of inertia I are false?
- I may be expressed in units of \(\mathrm{~kg m^2}\)
- I depends on the angular acceleration of the object as it rotates
- I depends on the location of the rotation axis relative to the particles that make up the object.
- I depends on the orientation of the rotation axis relative to the particles that make up the object.
Answer.
B.
References References
[1]
Numerical practice activities provided by BoxSand: https://boxsand.physics.oregonstate.edu/welcome.
