Can a Particle Sliding on a Rotating Rod Decrease in Distance Over Time?

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Homework Help Overview

The problem involves a particle of mass m that can slide along a rotating rod, which rotates about one end at a constant angular velocity. The objective is to analyze the motion of the particle, represented by a specific equation, and to explore conditions under which the distance from the rotation axis decreases over time. Gravity is neglected in this scenario.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants discuss the use of polar coordinates to describe the motion and question the implications of the particle being free to slide along the rod. There are inquiries about the forces acting on the particle and the role of the normal force in maintaining the particle's motion along the rod.

Discussion Status

The discussion is ongoing, with participants exploring various interpretations of the forces involved and the equations governing the motion. Some participants suggest analyzing the problem in different reference frames, while others express uncertainty about the implications of certain equations and forces.

Contextual Notes

There is mention of the need to consider both inertial and rotating frames, as well as the potential confusion arising from the Coriolis force. Participants are also navigating the constraints of the problem, such as the requirement for the particle to remain on the rod and the conditions under which its distance from the rotation axis may change.

  • #31
Pranav-Arora said:
For radial direction,
##F_r=ma_r \Rightarrow r\omega^2=\ddot{r}##. The solution of this differential is asked in the question.
To do the first part of the question, go from here.

edit: Oh wait, you said you did this bit already. sorry about that.
 
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  • #32
Pranav-Arora said:
:-p
r(0)=A

##r'(t)=-A\omega e^{-\omega t} \Rightarrow r'(0)=-A\omega##

Is this enough? I don't have the final answers.

You can also write that in case r'(0)=-ωr(0) the particle moves inward, that is r(t) decreases all the time . Note, it is interesting. The initial radial speed is the same as the azimuthal one...


ehild
 
  • #33
ehild said:
You can also write that in case r'(0)=-ωr(0) the particle moves inward, that is r(t) decreases all the time . Note, it is interesting. The initial radial speed is the same as the azimuthal one...


ehild

Thanks ehild! :smile:
 
  • #34
Hi everyone, sorry but i am a bit confused as to why radial acceleration is set to 0. Isn't the friction force from the rod pushing the mass inward, accounting for radial acceleration?
 
  • #35
kojo90 said:
Hi everyone, sorry but i am a bit confused as to why radial acceleration is set to 0. Isn't the friction force from the rod pushing the mass inward, accounting for radial acceleration?

What friction?
 
  • #36
well, just like the rod produces a perpendicular contact force (N), i would assume, as the ball wants to move radially out, there would be some friction involved. Or does the fact that the problem says, "slide along the rod freely" tell us to ignore this?
 
  • #37
Yes, "slide freely" means "no friction".
 

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