Uniform Circular Motion

Imagine that you are riding a bicycle with the handle bars turned in such a manner that your bike followed the path of a perfect circle with a constant radius. And suppose that as you rode, your bicycles speedometer maintained a constant reading of 1 m/s. In a situation like this, the motion of your bicycle would be described as uniform circular motion.

Uniform circular motion is the motion of an object in a circle with a constant or uniform speed.

Uniform circular motion - circular motion at a constant speed - is one of many forms of circular motion. An object moving in uniform circular motion would cover the same linear (distance in a straight line) distance in each second of time. When moving in a circle, an object traverses (moves) a distance around the perimeter of the circle.

If a car were to move in a circle with a constant speed of 5 m/s, then that car would travel 5 meters along the perimeter of the circle in each second of time. The distance of one complete cycle around the perimeter of a circle is known as the circumference.

Imagine a uniform speed of 10 m/s, if a circle had a circumference of 10 meters, then it would take the car 1 second to make a complete trip around the circle. At this uniform speed of 10 m/s, each trip around the 10 m circumference circle would require 1 second.

At 5 m/s, a circle with a circumference of 20 meters could be made in 4 seconds; and at this uniform speed, every cycle around the 20-m circumference of the circle would take the same time period of 4 seconds. This relationship between the circumference of a circle, the time to complete one cycle around the circle, and the speed of the object is merely an extension of the average speed equation:

Circumference = 2 pi radius = 2 π r

Combining these two equations above will lead to a new equation relating the speed of an object moving in uniform circular motion to the radius of the circle and the time to make one cycle around the circle. The time needed to make on trip around the circe is called the period. where R represents the radius of the circle and T represents the period.

This equation can be used as a recipe for problem solving. It also can be used to guide our thinking about the variables in the equation relate to each other. For instance, the equation suggests that for objects moving around circles of different radius in the same period, the object traversing the circle of larger radius must be traveling with the greatest speed. The average speed and the radius of the circle are directly proportional.

A twofold increase in radius corresponds to a twofold increase in speed; a threefold increase in radius corresponds to a three--fold increase in speed; and so on.

File translated from T_EX by T_TH, version 3.70.
On 20 Jan 2006, 10:00.