You may also like

Set Square

A triangle PQR, right angled at P, slides on a horizontal floor with Q and R in contact with perpendicular walls. What is the locus of P?

Mach Attack

Have you got the Mach knack? Discover the mathematics behind exceeding the sound barrier.

Construct the Solar System

Make an accurate diagram of the solar system and explore the concept of a grand conjunction.

Five Circuits, Seven Spins

Age 16 to 18
Challenge Level

A circular plate has radius one unit. It rolls around inside a rectangular tray, always touching the edge, and returns to its starting position after five circuits of the tray. During this time it rotates about its own centre by seven complete revolutions.

The motion is said to be periodic because it repeats itself over and over again after each five circuits and the length of the period is 5 circuits.

Can you find the dimensions of the tray? Is there more than one solution?

To help you with this question, you may like to read the article 'A Rolling Disc - Periodic Motion'