Instantanoeus axis of rotation

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Homework Help Overview

The problem involves a uniform rod of length l that is subjected to an impulse at right angles to its length, with the goal of determining the distance of the instantaneous center of rotation from the center of the rod. The discussion centers around concepts of impulse, momentum, and angular momentum in the context of rotational motion.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the relationship between impulse and momentum, questioning the correct formulation of initial angular momentum. There is also exploration of how torque relates to angular momentum and the implications of the instantaneous axis of rotation.

Discussion Status

Some participants have provided insights into the relationships between torque, impulse, and angular momentum. There is an ongoing exploration of the concept of "pure rotation" and how it applies to the motion of the rod. Multiple interpretations of the instantaneous axis are being considered.

Contextual Notes

Participants are navigating through the definitions and implications of impulse and torque, as well as the assumptions regarding the motion of the rod. There is a focus on understanding the dynamics of the system without reaching a definitive conclusion.

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Homework Statement


A uniform rod of length l is given an impulse at right angles to its length as shown. Find the distance of instantaneous centre of rotation from the centre of rod.
2dltzkm.png


Homework Equations





The Attempt at a Solution


Impulse=change in momentum
or Impulse=mvCM (Am i right here?)

I am not sure about this but i think i need to conserve angular momentum. But how should i make the equation for initial angular momentum. Should it be mvCMx or mvCM(x+d), d is the distance of instantaneous centre of rotation of rod from the CM.

Any help is appreciated!
 
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Pranav-Arora said:

Homework Statement


A uniform rod of length l is given an impulse at right angles to its length as shown. Find the distance of instantaneous centre of rotation from the centre of rod.
2dltzkm.png



The Attempt at a Solution


Impulse=change in momentum
or Impulse=mvCM (Am i right here?)

Impulse is FΔt,force multiplied by its time of action. And it is equal to the change of momentum. So the equation mvCM=Impulse is right.
Pranav-Arora said:
I am not sure about this but i think i need to conserve angular momentum. But how should i make the equation for initial angular momentum. Should it be mvCMx or mvCM(x+d), d is the distance of instantaneous centre of rotation of rod from the CM.

The applied impulse also means torque for time Δt: τΔt=Impulse*(x+d) The applied torque changes the angular momentum. You can calculate both the torque and angular momentum with respect to the instantaneous axis, considering the motion of the rod a pure rotation. Use the relation between torque and change of angular momentum:τ =I(Δω)/(Δt).You know ω from the initial speed of the CM: The CM will move around the instantaneous axis with angular speed ω=vCM/d.


ehild
 
Thanks ehild for your reply! :smile:

ehild said:
The applied impulse also means torque for time Δt: τΔt=Impulse*(x+d) The applied torque changes the angular momentum. You can calculate both the torque and angular momentum with respect to the instantaneous axis, considering the motion of the rod a pure rotation. Use the relation between torque and change of angular momentum:τ =I(Δω)/(Δt).You know ω from the initial speed of the CM: The CM will move around the instantaneous axis with angular speed ω=vCM/d.

I have got the answer using the relations you posted but i still don't understand what do you mean by "pure rotation"?
 
How is the instantaneous axis defined?

See picture. It shows a rod moved from position 1 to position 2 and rotated by 90°. You can do it by translating the rod from 1 to 2 and then rotating about the CM, or by rotating the whole rod about the instantaneous axis O.

ehild
 

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Last edited:
ehild said:
How is the instantaneous axis defined?

See picture. It shows a rod moved from position 1 to position 2 and rotated by 90°. You can do it by translating the rod from 1 to 2 and then rotating about the CM, or by rotating the whole rod about the instantaneous axis O.

ehild

Thank you ehild for the explanation!
 

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