How things work college course/Conceptual physics wikiquizzes/Uniform circular motion
Completion status: this resource is ~80% complete. 
The force required to sustain uniform circular motion is , where is acceleration and is the radius of the circle. The period of orbit, , is related to velocity by the fact that the distance traveled in one period of orbit is the circumference of the circle, .
You will be given the aforementioned equations as you are asked to do the following problems:
Plug in the numbers[edit]
 What is the acceleration (in m/s^{2}) of a particle that is traveling on a circle with a radius of 2 meters at a speed of 3 meters per second?
answer 


 What is the acceleration (in m/s^{2})of a particle that is traveling on a circle with a radius of 2 meters at a speed of 2 meters per second?
answer 


 What is the acceleration (in m/s^{2})of a particle that is traveling on a circle with a radius of 3 meters at a speed of 3 meters per second?
answer 


Proportional reasoning[edit]
The force required to sustain uniform circular motion is , where is acceleration and is the radius of the circle. The period of orbit, , is related to velocity by the fact that the distance traveled in one period of orbit is the circumference of the circle, .
Mr. Smith is using a string to swing a rock so fast that gravity may be neglected. What happens to the tension in the string when the velocity doubles?
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where k is a constant that depends on units. Adopting units such that F=v=1 initially, we see that k=1. In these units the force after changing v equals 2. The final force in these units is or 4 times the initial force. Answer: The force increases by a factor of 4 when the speed is doubled. 
Mr. Smith is using a string to swing a rock so fast that gravity may be neglected. What happens to the speed of the rock if the period is cut in half while the radius is tripled?
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where k is a constant that depends on units. Adopting units such that v=r=T initially, we see that k=1. In these units, the final radius is 3 and final period is 1/2. The final speed in these units is
Answer: The speed is increases by a factor of 6 when the the radius is tripled and the period is cut in half. Aside: If k=1 am I saying that 2π = 1? I hope not! Just measure velocity in meters per second, and measure time a madeup unit we shall call a blink. If one second equals 2π blinks consider what happens if the speed is seven meters per blink. OR DO I HAVE IT BACKWARDS???? 