![]() Each LED light traverses a circle of different radius. The strand is held at one end and spun rapidly in a circle. To illustrate, consider a strand of four LED lights positioned at various locations along the strand. 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. In fact, the average speed and the radius of the circle are directly proportional. 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. It also can be used to guide our thinking about the variables in the equation relate to each other. This equation, like all equations, can be used as an algebraic recipe for problem solving. Where R represents the radius of the circle and T represents the period. The circumference of any circle can be computed using from the radius according to the equation Circumference = 2*pi*RadiusĬombining 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 ( period). 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 stated in Unit 1 of The Physics Classroom. 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. At this uniform speed of 5 m/s, each cycle around the 5-m circumference circle would require 1 second. With a uniform speed of 5 m/s, a car could make a complete cycle around a circle that had a circumference of 5 meters. The distance of one complete cycle around the perimeter of a circle is known as the circumference. So if your car were to move in a circle with a constant speed of 5 m/s, then the car would travel 5 meters along the perimeter of the circle in each second of time. When moving in a circle, an object traverses a distance around the perimeter of the circle. An object moving in uniform circular motion would cover the same linear distance in each second of time. Uniform circular motion - circular motion at a constant speed - is one of many forms of circular motion. Uniform circular motion is the motion of an object in a circle with a constant or uniform speed. In such a situation as this, the motion of your car could be described as experiencing uniform circular motion. And suppose that as you drove, your speedometer maintained a constant reading of 10 mi/hr. Suppose that you were driving a car with the steering wheel turned in such a manner that your car followed the path of a perfect circle with a constant radius. Lesson 1 of this study will begin with the development of kinematic and dynamic ideas that can be used to describe and explain the motion of objects in circles. We will see that the beauty and power of physics lies in the fact that a few simple concepts and principles can be used to explain the mechanics of the entire universe. Kinematic concepts and motion principles will be applied to the motion of objects in circles and then extended to analyze the motion of such objects as roller coaster cars, a football player making a circular turn, and a planet orbiting the sun. In this unit, we will see that these same concepts and principles can also be used to describe and explain the motion of objects that either move in circles or can be approximated to be moving in circles. The same concepts and principles used to describe and explain the motion of an object can be used to describe and explain the parabolic motion of a projectile. ![]() ![]() The motion of a moving object can be explained using either Newton's Laws ( Unit 2 of The Physics Classroom) and vector principles ( Unit 3 of The Physics Classroom) or by means of the Work-Energy Theorem ( Unit 5 of The Physics Classroom). Any moving object can be described using the kinematic concepts discussed in Unit 1 of The Physics Classroom.
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