Average Velocity of a particle moving in a circle over a given interval

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Homework Help Overview

The discussion revolves around calculating the average velocity of a particle moving in a circular path over a specified time interval. Participants explore the definitions and implications of average velocity in the context of circular motion and straight-line displacement.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the definition of average velocity and its calculation based on displacement and time. There are attempts to relate circular motion to linear displacement, with questions about the path taken by the particle and the relevance of direction in velocity.

Discussion Status

There is an ongoing exploration of how to calculate average velocity, with some participants providing calculations and others questioning the assumptions made about the particle's movement. Guidance has been offered regarding the importance of retaining angle information in velocity calculations.

Contextual Notes

Some participants express confusion about the relationship between circular motion and linear displacement, particularly regarding the coordinates of the particle's position and the implications for average velocity. There is a focus on specific time intervals and the nature of the particle's path.

IAmPat
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Homework Statement



5Cyrk.png

Homework Equations



d = 2.5
c = pi*d = 7.854
velocity/s ?= c * 2 = 15.7079

The Attempt at a Solution


Since PR is 1/4 of the circle and the particle moves around the circle 2 times per second, I thought the average velocity would be 1/8th of the velocity that it's traveling. I'm really confused on this one.

EDIT: I only need to solve for (a), that's why I only have data pertaining to that. Not worried about B and C, but any intuition on those is welcome.
 
Last edited:
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What is the definition of average velocity?
 
zhermes said:
What is the definition of average velocity?

The change in x over time. The change in X is -1.25 right? and the time is 1/8 of a second... .125

dx/dt = -1.25/.125 = 10?

I'm not following
 
If someone were to show you two snapshots, the first showing the particle at P at time zero, and the second at point R at a time 1/8 second later, and you had no idea about the circular course, or what path the particle took to get from P to R, how would you go about finding the average velocity?
 
IAmPat said:
The change in x over time. The change in X is -1.25 right? and the time is 1/8 of a second... .125

Why just x?
 
gneill said:
Why just x?

What do you mean why just x?

The change in x is -1.25 and the change in time is 0.125 seconds, right?
 
IAmPat said:
What do you mean why just x?

The change in x is -1.25 and the change in time is 0.125 seconds, right?

So the particle didn't move along the circular path, but instead traveled a straight line along the x-axis and ended up at the origin? Is point R at the origin?
 
gneill said:
So the particle didn't move along the circular path, but instead traveled a straight line along the x-axis and ended up at the origin? Is point R at the origin?

It's at Y=1.25 and X=0. If I were to draw a straight line from P to R, the angles would be 45, 90 and 45 right? and the equation for the line would be:

1.25^2 + 1.25^2 = C^2
1.5625 + 1.5625 = C^2
3.125 = C^2
C = 1.767767

So ... The vector is (1.767767, 135 degrees)?
 
Last edited:
Okay! So you've got a distance vector. That gives you the displacement (magnitude of the vector) and the direction. Apparently the displacement happened in 1/8 second. So what's the average velocity vector?
 
  • #10
gneill said:
Okay! So you've got a distance vector. That gives you the displacement (magnitude of the vector) and the direction. Apparently the displacement happened in 1/8 second. So what's the average velocity vector?

So if the displacement is 1.767767 and happened in 1/8th. I assume I multiply the displacement by 8 to get the velocity per second...

So 14.1421 m/s?
 
  • #11
Yup!

Remember though, that velocity is a vector. So you want to retain the angle information in your answer.
 
  • #12
gneill said:
Yup!

Remember though, that velocity is a vector. So you want to retain the angle information in your answer.

Awesome. Your socratic method of teaching pissed me off to no end but it worked, and I'm very thankful for your help :-p
 
  • #13
IAmPat said:
Awesome. Your socratic method of teaching pissed me off to no end but it worked, and I'm very thankful for your help :-p

Heh. Bet you'll remember how to find the average velocity though!

Build a man a fire and he'll be warm for a day.
Set a man on fire and he'll be warm for the rest of his life!
 

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