# Weekly Brain Teaser | Consider a vertical wheel of radius 10 cm

Every week we feature a Brain Teaser or a thought-provoking question.

If you have one that you would like to share with fellow engineers, please email it to info@engineeringdaily.net.

So, here is this week’s,

Consider a vertical wheel of radius 10 cm. Now suppose a smaller wheel of radius 2 cm, is made to roll around the larger wheel in the same vertical plane while the larger wheel remains fixed.

What is the total number of rotations the smaller wheel makes when its center makes one complete rotation about the larger wheel?

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1. You’re right Kevin! Six rotations is correct. Your drawing showed that a point on the smaller wheel would sweep 432 degrees of arc before contacting the same point again with respect to the larger wheel. Interesting to note that a 2 cm radius circle would make five 360 degree rotations when traveling from start to end of a straight line that is 2π x 10cm long.

2. Yes – 5 rotations.

3. Nice drawings Kevin. Try the cardboard cutouts and you will find the answer is 5 rotations.

4. and yeah i used 10cm and 2cm as diameters instead of radius but its still proportional to the original problem

5. http://img504.imageshack.us/img504/959/math.jpg

i drew this in ms paint. are you still sure its 5 rotations?
imagine the large wheel is stationary and the smaller wheel is rolling along its edge.
the smaller wheel is marked to indicate how much it rotates.

i believe the first example is what most people think is the correct answer, but it isnt.