Rotational motion, frictionless.

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Discussion Overview

The discussion revolves around the dynamics of a cylinder with a rope wound around it, focusing on its motion and rotation under specific conditions, including negligible friction. Participants explore concepts related to linear and angular acceleration, the applicability of certain equations, and the behavior of a yo-yo in a zero-gravity environment.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant questions whether the cylinder can move forward with acceleration without rotating.
  • Another participant asserts that the equation Fr=Iα is always applicable, stating that the α=ar constraint is only necessary for rolling motion, which requires friction.
  • A participant expresses gratitude for the clarification regarding the applicability of rotation concepts, noting that their textbook did not address the distinction clearly.
  • Another participant introduces the idea of finding the instantaneous center of rotation as a relevant consideration in the discussion.
  • One participant suggests that a yo-yo in a zero-gravity environment will behave similarly to the cylinder when pulled, accelerating and spinning in the direction of the pull.

Areas of Agreement / Disagreement

Participants express differing views on the relationship between linear and angular motion in the absence of friction, with some asserting that Fr=Iα remains valid while others question the implications of slippage. The discussion does not reach a consensus on the applicability of certain equations under the given conditions.

Contextual Notes

There are unresolved assumptions regarding the effects of friction and the conditions under which the equations of motion apply. The discussion also highlights the need for clarity on the relationship between linear and angular accelerations in non-rolling scenarios.

azizlwl
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http://img444.imageshack.us/img444/8148/rollwx.jpg

A rope is wound around a cylinder of mass 4kg, and I=0.02kg.m2 about the cylinder axis.
The frictional force between table and cylinder is negligible.

Solution:
a=20/4=5.0m/s2
α=ar is not applicable when slippage occurs.


My question.
1.Is the cylinder moves forward with acceleration a without any rotation.
2. Is Fr=Iα is still applicable in this case, even though we know α=ar not applicable.
3. If we play yo-yo in zero gravity environment,how does the yo-yo behave when we pull it?

Thank you.
 
Last edited by a moderator:
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1. No, see 2.
2. Yes, Fr=Iα is always applicable. α=ar constraint is only needed for rolling, and is achieved via additional force, that being the force of friction. When no friction is present, you just compute angular and linear accelerations separately.
3. Yo-yo in zero-g will behave exactly the same as this test case. It will accelerate and spin in direction it's being pulled.
 
Thank you.
That really helpful since the book didn't say about rotation only a=αr is not applicable.
 
A nice question to ask here is to find the instantaneous centre of rotation.
 

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