HW10_prob3_three mass points

HW10_prob3_three mass points - Problem Three mass points...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
Problem Three mass points The three mass points are located at the vertices of the triangle shown in the f gure. The x , y and z variables are normalized by the factor a ,sotha t X = x/a , Y = y/a ,and Z = z/a . Z XY We are supposed to f nd the principal moments of inertia and a set of prin- cipal axes about the origin of the given body f xed frame. We start by f nding the elements of the inertia tensor in the given coordinate system. The general expression for the αβ component of the inertia tensor is I αβ = X i m i ( r 2 i δ αβ x x ) , (1) where the sum runs over all of the mass points in the body. For the body in question, there are three points with equal mass m ,sowecanwr ite I αβ = m 3 X i =1 ( r 2 i δ αβ x x ) , (2) and the points can be numbered any way you please. It is straightforward to evaluate the di f erent I αβ : I xx = m 3 X i =1 ( y 2 i + z 2 i )=1 1 ma 2 . (3) I yy = m 3 X i =1 ( x 2 i + z 2 i 1 ma 2 , (4) I zz = m 3 X i =1 ( x 2 i + y 2 i )=2 0 ma 2 , (5) I xy = I yx = m 3 X i =1 ( x i y i )= 4 ma 2 . (6) 1
Background image of page 1

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

View Full DocumentRight Arrow Icon
I xz = I zx = m 3 X i =1 ( x i z i )=0 , (7) I yz = I zy = m 3 X i =1 ( y i z i . (8) Thus, for the coordinate system in the f
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 12/19/2010 for the course PHYSICS ph 409 taught by Professor Wilemski during the Fall '10 term at Missouri S&T.

Page1 / 5

HW10_prob3_three mass points - Problem Three mass points...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online