{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

HW12 prob3 rod pivoting

# HW12 prob3 rod pivoting - Problem Kinetic Energy of a Rod(a...

This preview shows pages 1–2. Sign up to view the full content.

Problem: KineticEnergyo faRod (a) First we need to f nd the principal moments of the rod. This can be done with the origin either at the end of the rod (at the pivot) or at the center of the rod (the COM). There is a conceptual advantage with the latter approach, so we’ll take that route. Start with the general expression for the αβ component of the inertia tensor ( α , β = x , y , z ) I αβ = Z ρ ( r )( r 2 δ αβ x α x β ) d 3 r. (1) Note that r is measured from the origin of the body frame coordinate system, r 2 = x 2 + y 2 + z 2 ,and x x = x , x y = y , etc. For this rod, the linear mass density λ is constant, and its mass M is M =2 lλ, (2) where 2 l is the length of the rod. Given the geometry of the object, it is straightforward to use cartesian coordinates to do the required integrations. Let the rod lie along the z axis, so that x = y =0 along the length of the rod. The density can then be written as ρ ( r )= λδ ( x ) δ ( y ) ,u s ingD i racde l ta functions to constrain the x and y values. The easiest moment to evaluate is I zz , I = λ

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.

{[ snackBarMessage ]}

### Page1 / 3

HW12 prob3 rod pivoting - Problem Kinetic Energy of a Rod(a...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online