Can you solve it? Rotation, rotation, rotation

Gather round. Today’s puzzles are all about going in circles. Onward with the revolution!

1. Roll with it

Imagine a weight is being rolled along on logs, as below. The logs are all identical, perfect cylinders, and have a circumference of 1m.

How far does the weight move forward when a log completes one full rotation?

2. Locus pocus

Two searchlights with front-and-back lights are rotating clockwise at the same constant speed, as illustrated below. The beams are not parallel, and thus always intersect at a point.

What is the shape traced out by the intersection point?

3. Rover’s return

A Mars rover drives a full circle around the red planet. Assume that Mars is a perfect sphere, and the rover travels a full circumference, which is about 21,000 km

If the rover is 2m tall, how much further does the top of the rover travel compared to the bottom of the rover during its Martian circumnavigation?

a) Less than 15m

b) Between 15m and 1km

c) Between 1km and 1,000km

d) More than 1,000km

I’ll be back at 5pm UK with the answers.

PLEASE NO SPOILERS. Instead discuss your favourite circles.

Thanks to Shaheen Tonse for suggesting puzzle 2. The circumference of a circle is double the radius times pi, or 2πr.

I set a puzzle here every two weeks on a Monday. I’m always on the look-out for great puzzles. If you would like to suggest one, email me.

I give school talks about maths and puzzles (online and in person). If your school is interested please get in touch.