## Week 21

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