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Thread: Please discuss: Relating angular velocity to a sinusoidal function

  1. #1
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    Cool Please discuss: Relating angular velocity to a sinusoidal function

    I recently did an angular velocity problem where they gave the angular velocity (rate of rotation) and asked me to write it as a cosine function of the form:

    f(x) = a * cos [k (x - d)] + c

    A tutor told me that "k", the constant of horizontal compression, is also the angular velocity, so that:

    Period = (2pi) / abs(k)

    This means that the sinusoidal function is related to a circle and can be used to model angular velocity.

    Is there some theorem that relates the sinusoidal function to the unit circle? I am interested in knowing about this, and google returned nothing relevant. I would appreciate some further research into this.
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  2. #2
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    Re: Please discuss: Relating angular velocity to a sinusoidal function

    using $x$ and $y$ positions as functions of time for an object moving in a circle of radius $r$ centered at the origin, the following set of parametric equations model the uniform circular motion in two dimensions ...

    $x = r\cos(\omega t)$

    $y = r\sin(\omega t)$

    ... where the starting position is $(r,0)$ at time $t=0$ and angular velocity, $\omega = \dfrac{2\pi}{T}$

    animation link where one may adjust $r$ and $T$

    Uniform circular motion
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