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Properties of Uniform Circular Motion 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 each second of time. When moving in a circle, an object traverses a distance around the perimeter of the circle. 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. if the circle had a circumference of 20 meters, then it would take the car 4 seconds to make a complete cycle around the circle. Change the equation for average speed: Avg speed =distance/time =circumference/time and substitute 2**radius for circumference to get the equation: Avg Speed = 2**R Where T = period of time to complete 1 revolution Using this equation, it becomes clear that the radius of the circle is directly proportional to the average speed. For instance - if the radius of the circle were doubled, but the period to traverse the circumference remains the same, then the speed must double. Objects moving in uniform circular motion will have a constant speed. But does this mean that they will have a constant velocity? Recall that speed and velocity refer to two distinctly different quantities. Speed is a scalar quantity and velocity is a vector quantity. Velocity, being a vector, has both a magnitude and a direction. Since an object is moving in a circle, its direction is continuously changing. As the object rounds the circle, the direction of the velocity vector is different than it was the instant before. So while the magnitude of the velocity vector may be constant, the direction of the velocity vector is changing. Acceleration is defined as a change in velocity over a period of time, therefore an object with a change in the direction of the velocity has an acceleration, even if there is no change in speed, or the magnitude of the velocity. velocity = Avg Acceleration = time Vf - Vi t Remember the rules for adding or subtracting vectors: 1. 2. 3. the magnitude of the vectors does not change the directions of the vectors do not change for addition, but one vector is reversed for subtraction vectors must be placed head to tail to add or subtract For example: (Notice the direction of the acceleration.) This inward acceleration can be demonstrated with a cork accelerometer. The cork will move toward the direction of the acceleration. For an object moving in a circle, there must be an inward force acting upon it in order to cause its inward acceleration. This is sometimes referred to as the centripetal force requirement. The word "centripetal" (not to be confused with "centrifugal") means center-seeking. For objects moving in circular motion, there is a net force towards the center which causes the object to seek the center. To understand the need for a centripetal force, it is important to have a sturdy understanding of Newton's first law of motion - the law of inertia. The law of inertia states that ... "... objects in motion tend to stay in motion with the same speed and the same direction unless acted upon by an unbalanced force.“ According to Newton's first law of motion, it is the natural tendency of all moving objects to continue in motion in the same direction that they are moving ... unless some form of unbalanced force acts upon the object to deviate the its motion from its straight-line path. Objects will tend to naturally travel in straight lines; an unbalanced force is required to cause it to turn. The presence of the unbalanced force is required for objects to move in circles. Any object moving in a circle (or along a circular path) experiences a centripetal force; that is there must be some physical force pushing or pulling the object towards the center of the circle. This is the centripetal force requirement. The word "centripetal" is merely an adjective used to describe the direction of the force. The force could be a tensional force, a gravity force, a contact force, or even simply friction. The Forbidden F-Word When the subject of circular motion is discussed, it is not uncommon to hear mention of the word "centrifugal." Centrifugal, not to be confused with centripetal, means away from the center or outward. Have you ever felt a force pushing you outward as you made a sudden turn in a vehicle? Ask yourself the following questions: Does the sensation of being thrown outward from the center of a circle mean that there was definitely an outward force? If there is such an outward force on my body as I make a left-hand turn in an automobile, then what physical object is supplying the outward push or pull? And finally, could that sensation be explained in other ways which are more consistent with our understanding of Newton's laws?