- #1
DaalChawal
- 85
- 0
Calculating rates of two points moving along a circle
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Discussion Overview
The discussion revolves around calculating the rates of two particles moving along a circular path, focusing on their speeds and the implications of their directions of motion. The scope includes mathematical reasoning and conceptual clarification regarding the nature of speed versus velocity in circular motion.
Discussion Character
- Mathematical reasoning
- Conceptual clarification
- Debate/contested
Main Points Raised
- One participant proposes that the rates of closure and opening for two particles moving in opposite and the same directions can be expressed as $(v_1 + v_2)$ and $(v_1 - v_2)$, respectively.
- Another participant challenges the initial approach, arguing that the addition of speeds assumes linear motion, while circular motion involves changing direction, which affects velocity.
- A later reply reiterates the concern about treating the problem as one of velocity rather than speed, emphasizing the distinction between the two concepts.
- One participant claims to have derived specific speeds for the particles, stating $v_1 = 18 \, ft/sec$ and $v_2 = 12 \, ft/sec$, suggesting that others verify these results.
Areas of Agreement / Disagreement
Participants express disagreement regarding the treatment of speeds and velocities in the context of circular motion, with no consensus reached on the correct approach to the problem.
Contextual Notes
There is ambiguity regarding the definitions of speed and velocity as applied to circular motion, and the assumptions underlying the mathematical treatment of the problem remain unresolved.
- #2
skeeter
- 1,103
- 1
Let $v_1 > v_2$ be the respective speeds (rates) in feet per second of the two particles.
Moving in opposite directions, their rate of closure is $(v_1+v_2)$
Moving in the same direction, their rate of opening is $(v_1-v_2)$
Set up a system of two equations and solve for both speeds.
Moving in opposite directions, their rate of closure is $(v_1+v_2)$
Moving in the same direction, their rate of opening is $(v_1-v_2)$
Set up a system of two equations and solve for both speeds.
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- #3
DaalChawal
- 85
- 0
You have added them like they are moving on straight line...In circle velocity changes as direction is changing.
- #4
skeeter
- 1,103
- 1
DaalChawal said:
If the two particles move in opposite directions, the sum of their respective distances traveled in 5 seconds will be one full circumference length when they meet again.
If the two particles move in the same direction, the faster particle will move ahead of the slower particle, hence the difference between their respective distances traveled in 25 seconds will be one full circumference length when they meet again.
Using this method, I get $v_1 = 18 \, ft/sec$ and $v_2 = 12 \, ft/sec$. You can check the results yourself.
- #5
HOI
- 921
- 2
This problem has nothing to do "velocity". The problem asks for their speeds, not their velocities.
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