# Find final angular velocity of swinging meter stick

## Homework Statement

A meter stick is suspended vertically at a pivot point 25 cm from the top end. It is rotated on the pivot until it is horizontal and then released from rest. What will be its maximum angular velocity (in radians/second)?

## Homework Equations

I began by setting up a conservation of energy formula since the earth-stick system is not influenced by any nonconservative forces.
Ugrav(i) = Krot(f)
Mgh = (1/2)Iw2

## The Attempt at a Solution

When I try solving for w2 I become confused on what to use for h and for I on either side.

I'm thinking that h should be the vertical distance between the center mass at its initial and final points, which would be h = 1m - .25m = .75m

and for I: I = (1/3)ML2 where L is supposed to be the length of the rigid object; however, I do see that the pivot point is not at the end, so I do not know how to adjust this accordingly.

kuruman
Homework Helper
Gold Member
You need to use the parallel axes theorem to find the moment of inertia about the pivot. If you set the zero of potential energy at the pivot, then h is the distance from the pivot to the center of mass.

You need to use the parallel axes theorem to find the moment of inertia about the pivot. If you set the zero of potential energy at the pivot, then h is the distance from the pivot to the center of mass.

I am having trouble reasoning whether to put the center of mass at the .5m mark (middle of the meter stick) or whether the center of mass is the midpoint between the pivot and the end of the meter stick that is swinging downward.

kuruman