L09. Moment of Inertia for a Spherical Shell

We calculate the moment of inertia of a spherical shell about its center of mass. Then we use the parallel axis theorem to calculate the moment of inertia about an edge - the hanging disco ball.

[@thomasolson7447]

Anyone out there in the void wanna educate me. I'm probably going to hit Khan Academy Physics right quick and Chatgpt for my education. But this is exactly the sort of stuff I'm curious about right now. More specifically unit analysis and the polar graphs to some degree. This exampe in the video is a polar graph, so you got a clean set of rules for integration in 2d and apparently 3d. I like it. I'm looking at 2d graphs where the unit analysis of the area under the curve seems to be x*y (Force * m=Nm, m/s^2 * s=m/s). So Chat gpt tells me there are 4 kinds of graphs for 3d where x and y are independent and z is dependent. For the unit type of the volume under the curve I would just multiply the three axis units together?
I just added this from Chatgpt, it's nothing. Just examples I guess.
Electric Field: In electromagnetism, the electric field is a vector quantity that can be represented by a three-dimensional graph. The x and y axes can represent spatial dimensions, while the z axis represents the magnitude or strength of the electric field at each point in space.
(A/m)*m*m=A*m
Magnetic Field: Similar to the electric field, the magnetic field is another vector quantity that can be represented in a three-dimensional graph. The x and y axes represent spatial dimensions, and the z axis represents the magnitude or strength of the magnetic field at each point.
(A/m)*m*m=A*m
Wave Propagation: Graphs depicting the propagation of waves, such as sound waves or electromagnetic waves, often use three dimensions. The x and y axes represent spatial dimensions, while the z axis can represent the amplitude, intensity, or other characteristics of the wave at each point in space and time.
J/s·m^2*m*m=J/s·m^4 or W/m^2*m*m= W
Potential Energy Landscape: In various physical systems, potential energy landscapes can be visualized using three-dimensional graphs. The x and y axes represent spatial dimensions, while the z axis represents the potential energy of the system as a function of the positions in space.
J*m*m=J*m^2, or (kg⋅m^2/s^2)*m*m=kg⋅m^4/s^2