Bead sliding on a rotating rod

Click For Summary

Discussion Overview

The discussion revolves around the motion of a bead sliding on a rotating rod, specifically examining the curve traced by the bead from the perspective of an inertial observer. The scope includes theoretical exploration and mathematical reasoning related to non-inertial frames of reference.

Discussion Character

  • Exploratory
  • Technical explanation
  • Mathematical reasoning

Main Points Raised

  • One participant, shankar, proposes a differential equation to describe the bead's motion and suggests that the curve traced would be a cycloid, seeking clarification on this inference.
  • Another participant, Chet, questions whether the problem is a homework assignment.
  • Shankar clarifies that the discussion stems from a chapter on non-inertial frames in a mechanics textbook, prompting further inquiry about the curve.
  • A different participant references a logarithmic spiral as the implicit curve r(theta), suggesting an alternative interpretation of the bead's path.
  • Chet requests clarification on the derivation of the differential equation and points out potential errors in the proposed solution, specifically regarding the exponents in the equation.
  • Chet reiterates the need for correction, indicating that one of the exponents should be positive and suggesting the solution may involve hyperbolic cosine.
  • Shankar acknowledges a typo regarding the exponent and confirms that the radius is scaled, thanking Chet for the feedback.

Areas of Agreement / Disagreement

Participants express differing views on the nature of the curve traced by the bead, with some suggesting a cycloid and others proposing a logarithmic spiral. There is no consensus on the correct interpretation or solution to the problem.

Contextual Notes

There are unresolved aspects regarding the derivation of the differential equation and the assumptions made about the motion of the bead. The discussion includes potential errors in the proposed mathematical solutions.

shankarrg
Messages
3
Reaction score
0
Bead is at rest on a thin rod pivoted at one end. Bead is about a cm from the pivoted end of the rod. Rod now starts rotating with an uniform angular velocity w rad/sec.

1.What curve does the bead trace from the point of view of an inertial observer?

Here what i think... solution of the differential equation m*d^2(r)/dt^2= mrw^2

In the radial direction

r=Ae^(-wt)+Be^(-wt) , where A and B can be found out by the initial conditions. A=a/2, B=a/2

and in angular direction, theta =w*t

I think the curve would be cycloid. How to infer cycloid from the above equation

Regards
shankar
 
Physics news on Phys.org
Is this a homework problem?

Chet
 
No i was reading non inertial frames chapter in introduction to mechanics david kleppner there is an worked out example about finding the above equation i understood that but i started wondering about the curve it makes
 
Please show us how you arrived at your differential equation, and how you solved it. The solution as you've written it doesn't look correct (with the same exponent in both terms).

Chet
 
Chestermiller said:
Please show us how you arrived at your differential equation, and how you solved it. The solution as you've written it doesn't look correct (with the same exponent in both terms).

Chet

One of the exponents is supposed to be positive.
 
HomogenousCow said:
One of the exponents is supposed to be positive.
Yes. Otherwise, the solution looks OK (assuming that the radius has been scaled to the initial radius). We are talking about hyperbolic cosine here.

chet
 
Oh sorry was unaware that i made a typo . Yes i meant one exponent is positive and radius is scaled

Thanks for your reply chet
 

Similar threads

Graduate Bead sliding on a uniformly rotating wire
  • · Replies 37 ·
2
Replies
37
Views
6K
Undergrad A rod that falls while rotating from the end of a table
  • · Replies 2 ·
Replies
2
Views
2K
Bead on a rotating stick and the Lagrangian
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Mass dropped onto rotating disk
  • · Replies 5 ·
Replies
5
Views
3K
Undergrad Force on a rod attached to a pivot
  • · Replies 1 ·
Replies
1
Views
3K
Graduate Collision of a ball with a rod on a track
  • · Replies 13 ·
Replies
13
Views
3K
Undergrad Calculate the power generated by a rotating rod turning a generator
  • · Replies 12 ·
Replies
12
Views
3K
Bead Sliding on Rotating Rod after Motor is Turned Off
  • · Replies 17 ·
Replies
17
Views
4K
Graduate Bead on a rotating vertical ring
  • · Replies 9 ·
Replies
9
Views
15K
Understanding the Motion of a Bead on a Rotating Rod
  • · Replies 16 ·
Replies
16
Views
16K