Angular momentum along a sloping line

In summary, the conversation discusses finding the angular momentum of a 1.0 kg particle moving at a constant 3.5 m/s along the line y=0.62x+1.4. The formula L=Iw is used, but there is a problem with the relationship between x and y. The conversation suggests using the point where the trajectory crosses the y axis to simplify the calculation, as angular momentum will be conserved along the entire path. A formula for finding the perpendicular distance of a point from a line is also mentioned.
  • #1
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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  • #2
Firstly, how did you get this formula? By the definition?
Rethink your substitution for y. What is ##y## by definition?
 
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  • #3
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...
 
  • #4
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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  • #5
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?
 
  • #6
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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  • #7
Then thank you sir for your help! Really appreciated.
 
  • #8
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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  • #9
Thank you.
 

Related to Angular momentum along a sloping line

1. What is angular momentum along a sloping line?

Angular momentum along a sloping line refers to the rotational motion of an object along a line that is not horizontal. It takes into account the mass, velocity, and radius of the object as well as the angle of the slope.

2. How is angular momentum along a sloping line calculated?

The formula for calculating angular momentum along a sloping line is L = mvr sin(theta), where m is the mass of the object, v is the linear velocity, r is the distance from the object to the axis of rotation, and theta is the angle of the slope.

3. What factors affect the angular momentum along a sloping line?

The angular momentum along a sloping line is affected by the mass of the object, the linear velocity of the object, the distance from the object to the axis of rotation, and the angle of the slope. Changing any of these factors will result in a change in the object's angular momentum.

4. How does the angle of the slope affect the angular momentum along a sloping line?

The angle of the slope has a direct impact on the magnitude of the angular momentum along a sloping line. The greater the angle, the greater the sin(theta) term in the formula, resulting in a larger angular momentum. When the slope is vertical (theta = 90 degrees), the angular momentum is at its maximum.

5. Can the angular momentum along a sloping line be conserved?

Yes, the angular momentum along a sloping line can be conserved. In order for this to occur, the net torque on the object must be zero. This means that the forces acting on the object must be balanced, resulting in no change in angular momentum. This is known as the law of conservation of angular momentum.

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