Modelling Movement of Wheel Using Parametric Equations A particle of negligible size is lodged onto

Question

Modelling Movement of Wheel Using Parametric Equations A particle of negligible size is lodged onto the circumference of a circular wheel of radius $1$. Initially, the wheel is at rest with its lowest point at the origin. The initial position of the particle between the wheel and the floor (represented by the $x$-axis) is at the origin as well, as shown in the diagram below. The wheel begins to move from rest, rotating towards the positive $x-$direction in a clockwise manner. The position of the particle when the wheel has rotated by $	heta $ radians is denoted by the point $P$, as shown in the diagram below. Given that the curve $C$ is the path of $P$ on the $x-y$ plane, show that $C$ has the parametric equations $x=	heta -\sin 	heta $, $y=1-\cos 	heta $. find the range of values of $y$, sketch $C$, for $0\le 	heta \le 2\pi $, indicating clearly the exact coordinates of the endpoints and the maximum point.

Accepted Answer

$$x = 	heta - \sin	heta, \quad y = 1 - \cos	heta$$

NJC Parametric Equations Tutorial Q10

NJC Parametric Equations Tutorial Q10

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