** 21.T Volumes II; Total mass**

** Reference: ** Stewart 5.3, 13.4

** Keywords: ** Volume, solid of revolution, disks and washers,
cylindrical shells, mass, density, cylindrical coordinates

** Learning Objectives: ** The student will be able to:

- Set up integrals for the volume of a solid of revolution by both the method of disks and washers and the method of cylindrical shells
- Compute the volume by whichever method is most convenient for each particular problem
- Define mass and density and explain the relation between them
- Express as a triple integral the mass of a solid object (and evaluate in simple cases)
- For an axially symmetric density, express the mass as an integral in cylindrical coordinates (and evaluate in simple cases)

** 21.R
Centroids and moments of inertia I** <--(READ ME)

** Reference: **
*Don't Panic* Vol. I Chap. 15,
Stewart 13.3(review), 13.5, 13.7

** Keywords: ** Center of mass, centroid, moment of inertia

** Learning Objectives: ** The student will be able to:

- Compute the center of mass and the moments of inertia of a system of point masses
- Define the center of mass of a solid object, and express its components as triple integrals in rectangular coordinates
- Define the moment of inertia of a solid object with respect to a given axis, and express it as a triple integral in rectangular coordinates
- Express the moment of inertia about a symmetry axis as an integral over the radial coordinate