How many rotations of peddels per second?

[mmoadi]

Homework Statement

A bicycle drives on a straight road with a velocity v = 18 km/h. How many turns (rotations) of peddles per second must be carried out by cyclists, if the radius of the wheels r = 35 cm, and the ratio of the radii of front and rear gear wheels is 2:1?

Homework Equations

I used formula v=2(pi)r * f

The Attempt at a Solution

So, I have another problem which says:

I converted: 18km/h = 5m/s and 35cm = 0.35m, so now we have all units unified.

I plugged the numbers into the formula and got the result f= 2.27.

And now we have the ratio 2:1, and since the the front gear wheel is larger than the rear one I multiplied by 2 and got the FINAL result which is 4.55 turns of peddles per second.
Are my calculations correct?
Thank you for all the help!

 

[mgb_phys]

If the ratio of the gears is 2:1 doesn't that mean 2revs of the pedals to each rotation of the rear wheel?

 

[mmoadi]

So that mean that I have to divide by to and the correct final answer is f= 1.14?

 

[mgb_phys]

Yes -
Twice the radaii on the front cog means that it rotates once for 2 rotations of the back cog (and hence the back wheel) - this is the normal gearing for a bike (except the lowest gear on a mountain bike) - I thought the question had claimed the opposite.

 

[mmoadi]

Thank you for your help!