Assignment #4

Due: 23 November, 1998

Wheels Within Wheels

Suppose we roll a disk of radius 2 counterclockwise along the inside of a circle of radius 4 with centre at the origin, as in the diagram below.


1. If we start the disk off with its centre on the x-axis, what is the curve traced out by the point A on the disk, which is initially at (3,0)? [4]

Suppose all distances are in cm and the edge of the disk has a constant speed of 1 cm/s.

2. What is the speed of the point A when it is at (3,0)? at (0,1)? [3]

3. What is the maximum speed achieved by the point A? [3]

Please give all your reasoning in each of your answers!

Bonus. What does this have to do with astronomy? [1]

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