Angular momentum along a sloping line

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Homework Help Overview

The problem involves calculating the angular momentum of a particle moving along a specified linear path. The particle's mass and velocity are given, and the trajectory is defined by a linear equation in a two-dimensional plane.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants discuss the application of the angular momentum formula and question the appropriateness of substituting values for the variables involved. There is exploration of the relationship between the particle's position on the line and its angular momentum.

Discussion Status

Participants are actively engaging with the problem, raising questions about the definitions and relationships involved. Some guidance has been provided regarding the choice of points for calculations, and there is acknowledgment of the need for clarity in the approach.

Contextual Notes

There is mention of the conservation of angular momentum along the particle's path, and participants are considering the implications of using specific points for calculations. The discussion reflects uncertainty about the relationship between the trajectory and the angular momentum calculation.

rpthomps
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Homework Statement



A 1.0 kg particle is moving at a constant 3.5 m/s along the line y=0.62x +1.4, where x and y are in meters and where the motion is toward the positive x and y directions. Find its angular momentum about the origin2. Attempt at a solution##L=Iw\\\\L=myv\\\\L=(1)(0.62x+1.4)(3.5)##Not sure what to do with x though. If I set x=0, this just evaluates the momentum at a point not over the line. The line is infinite, so I would have thought the momentum evaluates to infinity as well but the answer is 4.2
 
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Firstly, how did you get this formula? By the definition?
Rethink your substitution for y. What is ##y## by definition?
 
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Suraj M said:
Firstly, how did you get this formula? By the definition?
Rethink your substitution for y. What is ##y## by definition?

You're right. There is a problem with my relationship.

Physics_Question.jpg


The trig part doesn't seem to simplify to nicely though...
 
rpthomps said:
You're right. There is a problem with my relationship.

Physics_Question.jpg


The trig part doesn't seem to simplify to nicely though...
What is this point P you have chosen? Just consider the point where the trajectory crosses the y axis.
 
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Can I use that position because angular momentum will be conserved for the whole trip and thus will be the same along the path of the mass and the position you suggested is the simplest to calculate?
 
rpthomps said:
Can I use that position because angular momentum will be conserved for the whole trip and thus will be the same along the path of the mass and the position you suggested is the simplest to calculate?
Yes.
 
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Then thank you sir for your help! Really appreciated.
 
OP, since you've got the answer, it might help you in the future to know the formula for the perpendicular distance of a point from a line, which would simplify the calculation as there would be no angle involved in the calculation.
Do you happen to have a formula like that? if you did you'll get your d and hence answer would just be mvd.
 
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Thank you.
 

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