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Math Help - Rolling Wheel

  1. #1
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    Rolling Wheel

    I am having a problem with the problem:
    A wheel of radius 1 meter rests on the x-axis with it's center on the y-axis. There is a spot on the rim at point (1,1). At time t=0 the wheel starts rolling on the x-axis towards positive infinity (to the right) at a rate of 1 radian per second. Find parametric equations describing the motion of
    (a) The center of the wheel.
    (b) The motion of the spot on the rim.
    I think I have part a figured out. x=t, y=1, as the center of the wheel will not go up or down and the arc length on a unit circle is the same as its measure in radians (please correct me if I am wrong)
    For b I am guessing that I can describe y with y=sin(t)+1, but I cannot figure out how to model x.
    Please point out any points on which I am incorrect, and give any assistance you can.
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  2. #2
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    Quote Originally Posted by Dotdash13 View Post
    I am having a problem with the problem:
    A wheel of radius 1 meter rests on the x-axis with it's center on the y-axis. There is a spot on the rim at point (1,1). At time t=0 the wheel starts rolling on the x-axis towards positive infinity (to the right) at a rate of 1 radian per second. Find parametric equations describing the motion of
    (a) The center of the wheel.
    (b) The motion of the spot on the rim.
    I think I have part a figured out. x=t, y=1, as the center of the wheel will not go up or down and the arc length on a unit circle is the same as its measure in radians (please correct me if I am wrong)
    For b I am guessing that I can describe y with y=sin(t)+1, but I cannot figure out how to model x.
    Please point out any points on which I am incorrect, and give any assistance you can.
    Have a look here: Cycloid - Wikipedia, the free encyclopedia
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