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)? 
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. What is the maximum speed achieved by the point A? 
Please give all your reasoning in each of your answers!
Bonus. What does this have to do with astronomy? 
Department of Mathematics
Maintained by Stefan Bilaniuk. Last updated 1999.12.03.