Center of Mass

# Center of Mass - Let’s work a couple of examples Example...

This preview shows pages 1–6. Sign up to view the full content.

Center of Mass In this section we are going to find the center of mass or centroid of a thin plate with uniform density ρ. The center of mass or centroid of a region is the point in which the region will be perfectly balanced horizontally if suspended from that point. So, let’s suppose that the plate is the region bounded by the two curves and on the interval [a,b]. So, we want to find the center of mass of the region below. We’ll first need the mass of this plate. The mass is, Next we’ll need the moments of the region. There are two moments, denoted by M x and M y . The moments measure the tendency of the region to rotate about the x and y -axis respectively. The moments are given by, Equations of Moments

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
The coordinates of the center of mass, , are then, Center of Mass Coordinates where,
Note that the density, ρ, of the plate cancels out and so isn’t really needed.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Let’s work a couple of examples. Example 1 Determine the center of mass for the region bounded by , on the interval . Solution Here is a sketch of the region with the center of mass denoted with a dot. Let’s first get the area of the region. Now, the moments (without density since it will just drop out) are, The coordinates of the center of mass are then, Again, note that we didn’t put in the density since it will cancel out. So, the center of mass for this region is . Example 2 Determine the center of mass for the region bounded by and . Solution The two curves intersect at and and here is a sketch of the region with the center of mass marked with a box. We’ll first get the area of the region. Now the moments, again without density, are The coordinates of the center of mass is then, The coordinates of the center of mass are then, ....
View Full Document

## This note was uploaded on 11/10/2011 for the course MATH 136 taught by Professor Prellis during the Fall '08 term at Rutgers.

### Page1 / 6

Center of Mass - Let’s work a couple of examples Example...

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online