Uniform Circular Motion

# Uniform Circular Motion - Uniform Circular Motion(U.C.M)...

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Uniform Circular Motion(U.C.M) defined as motion in a circle at a constant speed - not velocity since direction is constantly changing, thus the object ( mass tied to a string and whirling in a circle) is accelerating. this accereration is called centripetal acceleration and is always direction towards the center of a circle centripetal - center-seeking Centripetal acceleration (a c ) is found using the following formula: a c = v 2 r a c -- Centripetal acceleration v -- speed r -- radius the speed of an object undergoing U.C.M is found by: v = d = circumference = 2(pi)(r) or 2(pi)(r)(f) rperiodT Recall: f - frequency - in Hz - # of cycles per second T - period - in seconds - time for one cycle

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If an object is acceleration towards the center, there must be a force towards the center. This center-seeking force is called the centripetal force - defined as a force that causes an object to move in a circle.It can be supplied though a mass on a string; a frictionless force (car rounding a curve), or a gravitational force (moon around the Earth) U.C.M is really a special case of Newton's 2 nd law. F net = ma F c = ma c Also, v = 2(pi)(r) T Therefore, F c = 4(pi) 2 (r)(m)(f) 2 a is uniform in U.C.M thus the force that couses it must also be uniform. Example 1 A 150 g ball at the end of a string is revolving uniformly in a horizontal circle of radius 0.500 m. The ball makes exactly 2.00 revolutions per second. a.
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## This note was uploaded on 10/29/2008 for the course PHYS 2425 taught by Professor Kelt during the Spring '08 term at Northwest.

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Uniform Circular Motion - Uniform Circular Motion(U.C.M)...

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