(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A particle moves in a plane according to

x= Rsin(wt) = wRt

y= Rcos(wt) + R

where w and R are constants. This curve, called a cycloid, is the path traced out by a point on the rim of a wheel which rolls without slipping along the x-axis.

Question:

(a) Sketch the path.

(b) Calculate the instantaneous velocity and acceleration when the particle is at its maximum and minimum value of y.

2. Relevant equations

x= Rsin(wt) = wRt

y= Rcos(wt) + R

3. The attempt at a solution

I drew up the path of the particle, as a cycloid of course. No problem with that.

I am having problems understand part b, with relation to the curve.

I differentiated the given equations wrt to x.

i.e.

dy/dt = -Rw sin (wt)

dx/dt= Rw cos (wt) + wR

then i proceed to find dy/dx = [Rw sin (wt)]/[Rw cos (wt) + wR]

Y_{maximum}should be 2R (diameter of the rim of the wheel)

I also went ahead to find values of x which corresponds to the maximum and minimum values of y.

Values of X for maximum Y = 0, 2pie, ...

Values of X for minimum Y = pie, 3pie, ...

Instantaneous velocity is tangent of the curve of a position time graph, which is it the same as the graph i drew out?

Then back to the original question, the instantaneous velocity at maximum y is therefore 0? and instantaneous velocity at minimum y is infinity?

I know I have a conceptual error somewhere but I just can't figure it out.

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# Homework Help: Cycloid Particle question

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