Finding angular speed of a thin rod.

[Seraph404]

Homework Statement

A thin 1.0-meter-long rod pivoted at one end falls (rotates) from a horizantal position, starting from rest and with no friction. What is the angular speed of the rod when it is vertical?

Homework Equations

I (of the thin rod) = (1/3)ML^2

The Attempt at a Solution

I tried solving this problem using conservation of energy, but I'm not getting the right answer (5.4 rad/s).

For kinetic energy, I was using (1/2)I\omega^2; and for potential energy, I was using mgL. Then I solved for \omega. What's wrong with that?

 

[Doc Al]

In figuring out the change in PE of the rod, consider what happens to its center of mass.

 

[Seraph404]

It accelerates?

 

[Doc Al]

How does its position change? That determines the change in PE of the rod.

 

[Seraph404]

The CoM moves from a height of L to a height of L/2 ?

 

[Doc Al]

Good. So what's the change in PE of the rod?

 

[Seraph404]

MgL - Mg(L/2)

I got the answer now, thanks!