• Support PF! Buy your school textbooks, materials and every day products Here!

Torque/Rigid body rotation

  • Thread starter decerto
  • Start date
  • #1
87
2

Homework Statement


This is problem 7.7 from [kleppners mechanics book]http://books.google.ie/books?id=Hmq...rough a point on the rim of the hoop"&f=false but its also a general question on understanding this type of problem.

Homework Equations


L=Iω
dL/dt=ΩL=rxF


The Attempt at a Solution



The standard approach appears to be compute the angular momentum from Iω and find how it changes with respect to time, generally its ΩL where Ω is the precession about the axis, then compute the relevant torque and set them equal and solve for whatever your looking for.


My problems arises in 7.7 as the force creating the torque(the tension in the string) is at an angle to axis and the r from r x F is also at angle to the axis. So I'm not quite sure how I get the relevant force, I'm thinking it's as simple as r x (perp component of T) but I'm not 100%.

I'm also not sure since, I'm breaking down ω as a vector into components, perp and parallel to the hoop, then computing the spin angular momentum from the perp ω and ignoring the parallel ω one. But I'm not sure if you can just do that in this problem because the way the torque is setup, maybe I need to include the other component of angular momentum into it?.

Help would be much appreciated.

As they say solve it approximately with small angles, I assume that means cosx=1 and sinx=x


Right now for dL/dt i.e ΩL I have MR^2 ω^2 β
and for the torque I have with T=Mg torque=RMg(1+αβ)
 

Answers and Replies

  • #2
6,054
390
Google does not want to show that part of book anymore. You will have to reproduce the problem here to get any help.
 
  • #3
87
2
Google does not want to show that part of book anymore. You will have to reproduce the problem here to get any help.
Really? It shows me it just fine when I click on the link

http://www.maths.tcd.ie/~kovacs/Teaching/Mechanics/Kleppner-Kolenkow.pdf [Broken]

page 352 question 7.7
 
Last edited by a moderator:
  • #4
6,054
390
I have looked through the whole chapter in the book, and I have a question: how is the hoop different from a gyroscope tilted down?
 

Related Threads on Torque/Rigid body rotation

  • Last Post
Replies
1
Views
3K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
11
Views
2K
  • Last Post
Replies
1
Views
714
  • Last Post
Replies
4
Views
2K
  • Last Post
Replies
4
Views
618
  • Last Post
Replies
3
Views
4K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
3
Views
2K
  • Last Post
Replies
6
Views
2K
Top