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McMaster University
Paul Faure

September 11, 2013 Psych 3A03: Audition Tutorial 1: Harmonic Motion Uniform Circular Motion - For any object executing uniform circular motion, we expect the angle to increase linearly with time - In other words: , where  ω = angular rotation frequency (ω = 2πt), or the number of radians/s and t = time - - A describes the radius of the circle Circular Reasoning - π is an irrational number (i.e. has an infinite number of decimal places) - π = 180 ; 2π = 360 o - π is defined as the distance along the circumference from one side to the other of a circle with a radius (r) or length of one (r = 1) - The circumference (C) of a circle is defined as C = 2πr - Surface area (SA) = 4πr 2 - Spherical volume (V) = 4/3πr 3 The Unit Circle - Point P has coordinates x,y (starting from x=1, y=0) - cosθ describes how far P has moved along the x-axis from its starting coordinate of 1,0 - sinθ describes how far P has moved along the y-axis from its starting coordinate of 1,0 - x = cosθ; and y = sinθ Interesting Relationships of the Unit Circle - tanθ = sinθ/cosθ - This can be shown by rearranging the defined equations x = cosθ; and y = sinθ - Other interesting relations that emerge directly from the unit circle are:  sinθ = cos(90 – θ)  cosθ = sin(90 – θ)  sin θ +cos θ = 1 Const
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