Finding the Center of a circle

In summary, a particle moving horizontally in uniform circular motion with a velocity of -5.00 m/s and an acceleration of +10.0 m/s2 is located at coordinates (3.00 m, 3.00 m). Using the formula for centripetal acceleration, the radius of the circular path is calculated to be 2.5 m. Knowing the direction of the acceleration, the center of the circle can be located.
  • #1
KMjuniormint5
67
0
The question is:

A particle moves horizontally in uniform circular motion, over a horizontal xy plane. At one instant, it moves through the point at coordinates (3.00 m, 3.00 m) with a velocity of -5.00 m/s and an acceleration of +10.0 m/s2. What are the coordinates of the center of the circular path?

I know centripical acceleration is a = (v^2)/r

I know:
ax = 0 m/s^2
ay = 10 m/s^2

and . . .

vx = -5 m/s
vy = 0 m/s

where do i go from here?
 
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  • #2
KMjuniormint5 said:
I know centripical acceleration is a = (v^2)/r
What will that allow you to calculate?

I know:
ax = 0 m/s^2
ay = 10 m/s^2

and . . .

vx = -5 m/s
vy = 0 m/s
I assume that the directions were given?

Make use of that centripetal acceleration formula.
 
  • #3
ax = 0 m/s^2
ay = 10 m/s^2

and . . .

vx = -5 m/s
vy = 0 m/s

I am just assuming that from reading from the question . . .is that a safe assumption?

This is the question that I am asked:
A particle moves horizontally in uniform circular motion, over a horizontal xy plane. At one instant, it moves through the point at coordinates (3.00 m, 3.00 m) with a velocity of -5.00 m/s and an acceleration of +10.0 m/s2. What are the coordinates of the center of the circular path?

and what I did was find the accel. in the x and y direction and the velocity in the x and y velocity
 
  • #4
The question says "with a velocity of -5.00 m/s and an acceleration of +10.0 m/s2", but what direction? You assume the velocity is in the -x direction, but I see nothing in the problem statement that tells you that.

Perhaps this statement "A particle moves horizontally in uniform circular motion, over a horizontal xy plane" was supposed to read "A particle moves along the x-axis...". (If it's moving in a horizontal xy plane, then both x-axis and y-axis are horizontal.)

OK, let's assume your directions are correct. Now make use of the centripetal acceleration formula. You have v and a; find r.
 
  • #5
ahhhhh . . .there is another piece i left out . . "-5.00 i(hat) m/s and an acceleration of +10.0 j(hat) m/s2 "
. . .that is where I got my information from but even in that case would I still just do a direct plug in? so. . .

10 = 25/r and r having a value of 2.5m?
 
  • #6
KMjuniormint5 said:
ahhhhh . . .there is another piece i left out . . "-5.00 i(hat) m/s and an acceleration of +10.0 j(hat) m/s2 "
That makes all the difference! :smile:
. . .that is where I got my information from but even in that case would I still just do a direct plug in? so. . .

10 = 25/r and r having a value of 2.5m?
Right. Now use that to locate the center of the circle. (You know which way the acceleration points.)
 
  • #7
wow i was just making it way too hard. . .thank you so much Doc!
 

What is the definition of the center of a circle?

The center of a circle is a point located at an equal distance from all points along the circumference of the circle. It is often referred to as the "middle" of the circle.

How do you find the center of a circle?

To find the center of a circle, you need to measure the distance between two points on the circle's circumference. This distance is known as the radius. Then, find the midpoint between these two points, and that point is the center of the circle.

Can the center of a circle be located outside of the circle?

No, the center of a circle must always be located inside the circle. If the center is located outside of the circle, then it is not the center of that particular circle.

What is the importance of finding the center of a circle?

Finding the center of a circle is important for various reasons. It helps in accurately drawing and constructing circles, calculating the circumference and area of a circle, and understanding the symmetry and geometry of circles.

Is the center of a circle the same as the midpoint of the diameter?

Yes, the center of a circle is the same as the midpoint of the diameter. The diameter is a line segment that passes through the center and connects two points on the circumference. Therefore, the midpoint of the diameter is also the center of the circle.

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