Dynamics Question: Find Maximum Angular Velocity & Reaction at Pivot

[FChebli]

1. The problem statement

Hey everyone, I'm a new member here... I'd be grateful if you attempt to solve my following question:

A slender rod of length l is pivoted about a point C located at a distance b from its center G. It's released from rest in a horizontal position and swings freely. Determine (a) the distance b for which the angular velocity of the rod as it passes through a vertical position is maximum, (b) the corresponding values of its angular velocity and of the reaction at C.

Homework Equations

KE = T = 1/2 m V2
PE = V = m g h

The Attempt at a Solution

No idea! :S

 

[Doc Al]

I assume that the rod is uniform and that you're just trying to find the optimal pivot point.

Hint: Energy is conserved. How would you express the rotational kinetic energy of the rod?

 

[FChebli]

KE = 1/2 I w2?
Do I get the distance b (the distance from point C to the center G of the rod) using PE?
And thank you for the hint...

 

[Doc Al]

KE = 1/2 I w2?

Right.

Do I get the distance b (the distance from point C to the center G of the rod) using PE?

You'll have to solve for the distance b using the conditions given. The first step is to write an expression for conservation of energy. (Yes, you'll need PE as well as KE.)