A point moves in X−Y plane according to X=a sin(wt) and Y=a (1−cos(wt)). What path will the particle follow?

1 Answer
May 16, 2018

This is a circle of radius abs a, centred on X,Y = 0, a

Explanation:

X=a sin(wt), qquad Y=a (1−cos(wt)

implies sin omega t = X/a, qquad cos omega t = 1- Y/a

From the Pythagorean identity:

(X/a)^2 + ( 1- Y/a)^2 = 1

(X/a)^2 + ( Y/a - a/a)^2 = 1

X^2 + ( Y - a)^2 = a^2

This is a circle of radius abs a, centred on X,Y = 0, a