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