Uniform solid disk equations

  • Thread starter aborder
  • Start date
  • #1
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Homework Statement



A uniform solid disk of radius R and mass M is free to rotate on a frictionless pivot through a point on its rim (see figure below). The disk is released from rest in the position shown by the copper-colored circle.
10-p-053.gif



(a) What is the speed of its center of mass when the disk reaches the position indicated by the dashed circle? (Use any variable or symbol stated above along with the following as necessary: g.)

(b) What is the speed of the lowest point on the disk in the dashed position? (Use any variable or symbol stated above along with the following as necessary: g.)

(c) Repeat part (a) using a uniform hoop of mass M. (Use any variable or symbol stated above along with the following as necessary: g.)

Homework Equations



KEf + Uf = KEi + Ui
1/2Iω2
Impulse for disk = 1/3MR2
Vcm = Rω
KE = 1/2MV2
U = mgR

The Attempt at a Solution



Part A I got the right answer of [itex]\sqrt{}4gR/3[/itex]

Part B is giving me some issues and I suppose I am not sure where to go with it.

Part C I figured I could use the same method as part A, but for some reason, I get [itex]\sqrt{}2gR[/itex] and that is no good.
 

Answers and Replies

  • #2
998
15
All you have to do for the hoop is to use the same method as you did for the disc but with the moment of inertia for the hoop. If you show your work one can help you better.
 

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