How Does a Man Walking on a Merry-Go-Round Affect Its Motion?

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Homework Help Overview

The discussion revolves around the dynamics of a man walking on the edge of a merry-go-round, focusing on angular momentum and the effects of friction. The problem includes questions about angular velocity, rotation angle, and friction coefficient, with the system starting from rest.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the application of conservation of angular momentum and question the presence of torque in the system. There are attempts to clarify the role of friction and its impact on angular velocity.

Discussion Status

The discussion is active, with participants exploring different interpretations of angular momentum conservation and the implications of friction. Some guidance has been offered regarding the conditions under which angular momentum is conserved.

Contextual Notes

Participants are navigating the assumptions related to external torque and the effects of friction on the system's motion. There is a lack of explicit consensus on the implications of these factors.

asafbuch
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1. A man with mass m walks with a constant velocity v with respect to the ground on the edge of a marry-go-round that has a radius of R and moment of inertia I. The system starts from rest.
a) what is the angular velocity of the marry-go-round?
b) when the man completes a full cycle (returns to its initial position) at what angle did the marry-go-round rotate?
c)what is the friction coefficient between the man and the marry-go-round for the man not to get off the marry-go-round?



2. No relevant equations.



3. I tried to use conservation of angular momentum and got this:
I[tex]\omega[/tex]+mR2v/R=0
 
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welcome to pf!

hi asafbuch! welcome to pf! :smile:

(have an omega: ω and btw it's "merry-go-round" :wink:)
asafbuch said:
3. I tried to use conservation of angular momentum and got this:

that's right!

so ω = … ? :smile:​
 
I thought so... but shouldn't there be any torque?

If there is a conservation of angular momentum than there is no torque acting on the marry-go-round, means there is no friction between the man and the marry-go-round...
but if there is a torque (and thus a friction) than you don't have a constant angular velocity...

whats wrong with the theory?
 
hi asafbuch! :wink:

there will be conservation of angular momentum about any point if there is no external torque about that point …

the external friction is at the centre (and so has zero torque about the centre), so angular momentum will be conserved about the centre :smile:

(the friction between the man and the merry-go-round is an internal torque, so it doesn't matter :wink:)
 
oh, thank you tiny-tim!
 

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