Thread: 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 $\displaystyle t=0$ 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. $\displaystyle x=t, y=1$, 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 $\displaystyle y=sin(t)+1$, 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.

Originally Posted by Dotdash13

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 $\displaystyle t=0$ 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. $\displaystyle x=t, y=1$, 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 $\displaystyle y=sin(t)+1$, 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