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Uniform Circular Motion Basic Principles & Formulas

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Uniform Circular Motion Principles Object moves at a constant speed (speed = scalar quantity) Object’s velocity is constantly changing (velocity = vector quantity) due to a continuous change in direction Velocity is tangent to circular motion While in motion, there is a force and an acceleration being applied to the object

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Uniform Circular Motion Terms & Formulas Period (T) = time it takes to make 1 revolution (time to travel circumference). Period may be given, obvious or determined by time/revolutions ex. 25 rev. in 10 sec. T = 10/25 .4 sec (T = 1/f) Frequency (f) = number of revolutions made in 1 sec. (f = 1/T) units = Hz (Period & Frequency are Inversely Related)

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Uniform Circular Motion Diagram Acceleration & Force = Parallel to Radius / Velocity = Perpendicular to Radius r v F a

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Uniform Circular Motion Questions Q = While moving in a circular path, if string breaks, in what direction will the object travel? A = In a straight line, perp. to radius (Law of Inertia; resistance to change) Q = In what direction is the force? A = Inward Q = In what direction is the acceleration? A = Inward

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Uniform Circular Motion Terms & Formulas Velocity (v) = d or 2πr t T Acceleration (a) =v² r circumference Time to travel around circumference once

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Uniform Circular Motion Terms & Formulas Force (F) =ma or mv² r Remember, mass must be in Kg!

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UCM Example Problem A 615 kg race car completes 1.00 lap in 14.3 sec around a circular track with a radius of 50.0 m. What is the car’s T, f, v, a, F (on tires)? T = 14.3/1.00 = 14.3 f = 1.00/14.3 = 0.0699 Hz

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UCM Example Problem (cont.) V = (2)(π)(50.0) 14.3 = 22.0 m/s a = (22.0 m/s)² 50.0 = 9.68 m/s²

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UCM Example Problem (cont.) F (on tires) = (615 kg)(22.0 m/s)² 50.0 m = 5,950 N

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