This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: 3/27/08 Physics 201, UWMadison 1 Uniform Circular Motion 3/27/08 Physics 201, UWMadison 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, UWMadison 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, UWMadison 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, UWMadison 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 π1 1 sin cos θ 3/27/08 Physics 201, UWMadison 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, UWMadison 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...
View
Full
Document
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.
 Spring '08
 Walker
 Physics, Acceleration, Circular Motion

Click to edit the document details