What is the total kinetic energy of the rod?

[ccarit3007]

Homework Statement

Uniform rod rotates at axel. What is the total kinetic energy of the rod?

Homework Equations

deltaKrot = 1/2Iw^2
deltaKtrans = 1/2mv^2

The Attempt at a Solution

I believe the rod has both rotational as well as translation energy because the rod is not rotating about its center of mass. I end up getting 1/2ML^2w^2+1/2Mv^2 which is not the answer choices. (The answer is B).

 

[Doc Al]

I believe the rod has both rotational as well as translation energy because the rod is not rotating about its center of mass.

You can view the rod as having both rotational KE about the center of mass and translational KE of the center of mass. Or you can view the rod as in pure rotation about the given axis. Your choice. Either way, the answer will be the same.

I end up getting 1/2ML^2w^2+1/2Mv^2 which is not the answer choices.

Two points: (1) How did you get that expression for the rotational KE? (2) Realize that ω and v are related. Express everything in terms of ω.