### 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]*

Department of Mathematics
Trent University

Maintained by Stefan Bilaniuk. Last updated 1999.12.03.