Find final angular velocity of swinging meter stick

  • Thread starter makks
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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.
 

Answers and Replies

  • #2
kuruman
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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.
 
  • #3
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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.
 
  • #4
kuruman
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The center of mass of a uniform stick is the midpoint of the stick. This comes straight from the definition of center of mass which has no reference to a pivot. In other words, if you hang a stick from a pivot, the stick's center of mass will not suddenly shift to a new position. This is true for any extended massive object. Once you find its CM, that's it unless you change the distribution of the mass.
 

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