A small wheel of radius r is situated at the top of a ramp having an angle θ = π/3 rad At t = 0 the wheel is at rest and then it starts to rotate clockwise in the positive x direction with constant angular velocity ω.
Find the parametric equations of the x and y coordinates of the point as a function of time, for t > 0. Using Pythagoras’ theorem or
otherwise verify your formulas at the points xp(T) and yp(T), where T = 2π/ω.
I assume that the wheel does in fact start rolling down the ramp as it rotates.
We can assume that the top of the ramp is at (0,0).
Now, we know the cycloid of radius r is
x = r(t-sin t)
y = r(1-cos t))
Now we need to rotate the whole coordinate frame by -π/3, which I assume you
(a) know how to do
or (b) can read about.