Unit Kinematics Module Uniform Circular Motion page 1 of 2 Describing Uniform Circular Motion For uniform circular motion position can be described by an angle and a distance R from the origin In Cartesian coordinates x R cos and y R sin In uniform circular motion the direction of the velocity vector is tangent to the circle For an object in uniform circular motion the magnitude of its acceleration vector v2 The direction of the acceleration vector is centripetal or towards the R center is a An object traveling in a circle with uniform speed is in uniform circular motion The dot indicates the position of an object in the diagram The position can be described by a distance R and an angle from the origin In Cartesian coordinates x R cos and y R sin The period of the object is the time required for one cycle The object s frequency is the number of periods completed in one second The direction of the velocity vector of an object in circular motion is always tangent to the circle Its magnitude is constant since the motion is uniform Even though the speed of an object in uniform circular motion is constant the acceleration vector is not zero The direction of the velocity vector dv changes with time so acceleration a is not dt zero The triangle made by the position vectors is similar to the triangle made by the velocity vectors Given similar triangles you can write the equation r v Rearranging and taking the limit as t R v approaches zero allows you to solve for the v2 The magnitude of the acceleration vector R direction of the acceleration vector is the same as the direction of v The direction of a is toward the center of the circle or centripetal If the direction were not centripetal the object would move in a direction tangent to the circle www thinkwell com info thinkwell com Copyright 2001 Thinkwell Corp All Rights Reserved 1820 doc rev 03 28 2001 Unit Kinematics Module Uniform Circular Motion page 2 of 2 Describing Uniform Circular Motion Imagine a child going around a merry go round with a radius 2 m and a period of 3 s The child s velocity is the ratio of the distance traveled which is the circumference of the merrygo round 2 R 2 2 m and time or in this case the period T 3 s v2 In this example R the child feels an acceleration that is nearly equal to that of gravity The acceleration is given by www thinkwell com info thinkwell com Copyright 2001 Thinkwell Corp All Rights Reserved 1820 doc rev 03 28 2001
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