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McMaster University
Psychology
PSYCH 3A03
Paul Faure
Fall
Description
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 xaxis from its starting
coordinate of 1,0
 sinθ describes how far P has moved along the yaxis 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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