A farmer has a yellow tractor whose front tires have a radius of 40 cm and the rear tires have a radius of 1.20 m. When the front wheels have completed 10 revolutions, how many revolutions will the rear tires have completed?


Rfront = 40 cm = 0.4 m
Rrear = 1.2 m

φfront = 10 vueltas
φrear = ? vueltas


Since the tires have different radii, while the bigger rear tires complete one revolution the smaller front tires will complete more than one revolution, but regardless of the number of revolutions each one does, they both always travel the same distance. Therefore:

Sfront=Srear φfront · Rfront = φrear · Rrear

If the front tires have completed 10 revolutions, the angular position of these tires will be 10 times the angle of a full circumference, or what is the same 10 times 2π:

φfront=10 revolution · 2π rad/revolution=20π rad

So, the angular position of the rear tires is:

φfront · Rfront = φrear · Rrear φfront =φfront · RfrontRrearφrear=20π·0.41.2φrear=6.67π rad

If each revolution is 2π rad, then the rear tires revolution will be:

No. revolutions=6.67π2π=3.33 

Formulas worksheet

These are the main formulas that you must know to solve this exercise. If you are not clear about their meaning, we recommend you to check the theory in the corresponding sections. Furthermore, you will find in them, under the Formulas tab, the codes that will allow you to integrate these equations in external programs like Word or Mathematica.

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