CircularMotion - Physics 201 UW-Madison 1 Uniform Circular...

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Unformatted text preview: 3/27/08 Physics 201, UW-Madison 1 Uniform Circular Motion 3/27/08 Physics 201, UW-Madison 2 What is UCM? What is UCM? Motion in a circle with: Constant Radius R Constant Speed | v | Velocity is NOT constant (direction is changing) There is acceleration! R v x y 3/27/08 Physics 201, UW-Madison 3 How can we describe UCM? How can we describe UCM? In general, one coordinate system is as good as any other: Cartesian: » (x,y) [position] » (v x ,v y ) [velocity] Polar: » (R, θ ) [position] » (v R , ω ) [velocity] In UCM: R is constant (hence v R = 0 ). ω (angular velocity) is constant. Polar coordinates are a natural way to describe UCM! Polar coordinates are a natural way to describe UCM! R v x y θ 3/27/08 Physics 201, UW-Madison 4 Polar Coordinates: Polar Coordinates: The arc length s (distance along the circumference) is related to the angle in a simple way: s = R θ , where θ is the angular displacement . units of θ are called radians . For one complete revolution: 2 π R = R θ c θ c = 2 π θ has period 2 π . 1 revolution = 2 1 revolution = 2 π π radians radians R v x y θ 3/27/08 Physics 201, UW-Madison 5 Polar Coordinates... Polar Coordinates... x = R cos θ y = R sin θ R x y (x,y) θ π / 2 π 3 π /2 2 π-1 1 sin cos θ 3/27/08 Physics 201, UW-Madison 6 Polar Coordinates... Polar Coordinates... In Cartesian coordinates, we say velocity dx/dt = v . x = vt In polar coordinates, angular velocity d θ /dt = ω . θ = ω t ω has units of radians/second . Displacement s = vt . but s = R θ = R ω t, so: R v x y s θ = ω t v = ω R 3/27/08 Physics 201, UW-Madison 7 Period and Frequency Period and Frequency Recall that 1 revolution = 2 π radians frequency (f) = revolutions / second (a) angular velocity ( ω ) = radians / second (b) By combining (a) and (b) ω...
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This note was uploaded on 03/27/2008 for the course PHYS 201 taught by Professor Walker during the Spring '08 term at University of Wisconsin.

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CircularMotion - Physics 201 UW-Madison 1 Uniform Circular...

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