What is the center of circular path?

[GingerBread27]

A particle moves horizontally in uniform circular motion, over a horizontal xy plane. At one instant, it moves through the point at coordinates (7.00 m, 7.00 m) with a velocity of -5.00 i m/s and an acceleration of -12.0 j m/s2. What are the coordinates of the center of the circular path?

I figured you'd have to find the radius and then it would be a simple problem but I was wrong. How is this done.

 

[Janitor]

Hints:

The center will be on a line perpendicular to the velocity. You are given that the velocity is in the -x direction, so the x coordinate of the center will be the same as the x coordinate of the particle.

To get the y coordinate of the center, note that the acceleration is in the -y direction, so the center will have a y coordinate less than the y coordinate of the particle. How much less than? Use the formula relating radius and speed and acceleration for uniform circular motion.

 

[e(ho0n3]

Explain how "a particle moves horizontally in uniform circular motion" as well as "a horizontal xy plane". You could just say "A particle is moving in uniform circular motion on the xy-plane...". Anywho, finding the radius is the key to solving this problem. What exactly are you having trouble with?

 

[GingerBread27]

For the y coordinate I get -2 and that is incorrect. I'm using a=v^2/r using a=-15 and v=-5. What am I doing wrong.

 

[0aNoMaLi7]

Again...i have the same problem as you for my class 'GingerBread27'...I know the people here are keen on YOU solving the problem...NOT someone else but I just figured it out and figured I'd give you a heads up if you hadn't yet.

This is a problem in visualization. With the help of "Janitor" and about 15 minutes of staring I was able to nail this problem. I've provided a diagram to get you on your way. It should help. Like "Janitor" suggested use the

a = (v^2)/ r ---- you have all the variables you need...

good luck

here's the diagram to assist (below):

 

[GingerBread27]

What in the world am I not seeing. I know the y-coordinate must be less than 7 but when I plug in the numbers and all I get -2 and it's not correct.

 

[0aNoMaLi7]

oh I am sorry...the coordinate in my problem is (5,5) i also have different 'a' and 'v' values...one moment...ill spell it out for you

 

[0aNoMaLi7]

the end to your frustrations:

your coordinate is (7,7)
your velocity vector is -5
your acceleration vector is -12

using the relationship a = (v^2)/r
REARRANGE: r = (v^2)/a

lets call r 'VALUE'

the x-coordinate we know is 7

therefore, subtract 'VALUE' from 7 for y ...

now?

 

[0aNoMaLi7]

yes? no? maybe?

 

[GingerBread27]

yes!

 

[Janitor]

Well done.

As an aside, don't get too hung up on signs when using the formula for uniform circular motion. It is not intended to be a truly vectorial formula in the form that you are using it (though it can be cast into true vector form if you really want to do so), so you can cavalierly throw away the negative signs in this problem, and use other arguments to handle the kind of directional information you lose when you cast out negatives.