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

In summary, the conversation is about finding the average velocity of a particle moving along a circular path. The equation for the velocity is c * 2 = 15.7079, and the definition of average velocity is the change in x over time. The conversation also discusses finding the displacement and direction of the particle, and determining the average velocity vector. Through a series of questions and answers, the participant is able to successfully calculate the average velocity of the particle.
  • #1
IAmPat
29
0

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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  • #2
What is the definition of average velocity?
 
  • #3
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
 
  • #4
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?
 
  • #5
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?
 
  • #6
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?
 
  • #7
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?
 
  • #8
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)?
 
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  • #9
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 :tongue:
 
  • #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 :tongue:

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!
 

What is the average velocity of a particle moving in a circle over a given interval?

The average velocity of a particle moving in a circle over a given interval is the total displacement of the particle divided by the total time taken for the motion. It is a vector quantity that describes the rate of change of position of the particle in a circular path.

How is the average velocity of a particle moving in a circle calculated?

To calculate the average velocity of a particle moving in a circle, we need to find the total displacement of the particle over the given interval and divide it by the total time taken for the motion. This can be represented as:
Average velocity = (Total displacement)/ (Total time taken)

Does the average velocity of a particle moving in a circle change?

Yes, the average velocity of a particle moving in a circle can change if the speed or direction of the particle changes. This is because the total displacement and total time taken for the motion will also change, resulting in a different average velocity.

How is the average velocity of a particle moving in a circle different from the instantaneous velocity?

The average velocity of a particle moving in a circle is the average rate of change of the particle's position over a given interval. On the other hand, instantaneous velocity is the velocity of the particle at a specific moment in time. This means that while average velocity takes into account the entire motion of the particle, instantaneous velocity only considers a single point in time.

Can the average velocity of a particle moving in a circle be negative?

Yes, the average velocity of a particle moving in a circle can be negative if the particle moves in a clockwise direction. This is because the direction of motion is taken into account when calculating average velocity, and negative velocity indicates motion in the opposite direction of a chosen positive direction.

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