Calculating rates of two points moving along a circle

In summary, the conversation discusses the respective speeds of two particles moving in opposite and same directions. It mentions that the rate of closure when moving in opposite directions is the sum of their speeds, and the rate of opening when moving in the same direction is the difference between their speeds. A system of equations is set up and the speeds are solved to be $v_1 = 18 \, ft/sec$ and $v_2 = 12 \, ft/sec$. The problem is about speeds, not velocities.
  • #1
DaalChawal
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Question 3
 
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  • #2
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.
 
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  • #3
You have added them like they are moving on straight line...In circle velocity changes as direction is changing.
 
  • #4
DaalChawal said:
You have added them like they are moving on straight line...In circle velocity changes as direction is changing.

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
This problem has nothing to do "velocity". The problem asks for their speeds, not their velocities.
 

What is the formula for calculating the rate of two points moving along a circle?

The formula for calculating the rate of two points moving along a circle is: rate = (angular displacement)/(time interval).

How do you determine the angular displacement of two points on a circle?

The angular displacement can be determined by finding the difference between the initial and final angles of the points on the circle. This can be measured in degrees or radians.

Is the rate of two points moving along a circle always constant?

No, the rate of two points moving along a circle can vary depending on the speed and direction of the points. If the points are moving at a constant angular velocity, then the rate will remain constant. However, if the points are accelerating or decelerating, the rate will change.

Can the rate of two points on a circle be negative?

Yes, the rate of two points on a circle can be negative if the points are moving in opposite directions. This means that one point is moving clockwise while the other is moving counterclockwise. The negative sign indicates the direction of movement.

How does the radius of the circle affect the rate of two points moving along it?

The radius of the circle does not directly affect the rate of two points moving along it. However, a larger radius will result in a longer distance traveled for the same angular displacement, which will result in a higher rate. Similarly, a smaller radius will result in a shorter distance traveled and a lower rate.

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