A cyclist moves with your bike straight

Classical Mechanics Level 1

A bike moves at a rate of $\si{18\ \kilo\meter/\hour}$ . The rear tire has a diameter of $\si{70\ \centi\meter}$ and has a toothwheel of diameter $\si{7\ \centi\meter}$ . The sprocket (the gear that's turned by the pedals) has diameter $\si{20\ \centi\meter}$ . Both gears are connected by the chain and there is no slippage between the chain and either gear. Under these conditions, how many times do the pedals revolve per minute?

In this matter, assume $\pi = 3$ .

25 0.25 5 50 2.5

1 solution

Ajit Athle
Jul 20, 2016

18 km/hr = 5 m/s = ω r = ω (35/100) or ω = 100/7 rad/s = 6000/7 °/s if π =3. Since we are assuming no slippage, (6000/7)*7 = 20 * Ω or Ω = 300 °/s = 300/360 Rev/s = 5/6 Rev/s = 50 Rev/min

Gear ratio "20:7" equals about 2.9. Wheel diameter 70 x pi=2.1 meters. (Since pi is 3 not 3.1415eternity.)

Wheel dia*gear=2.1 x 2.9 = 6.1 m/revolution.

18km/h = 5 m/s =300 m/min So there for 300/6.1=50 ish r/min or we have a cadence of 50.

I hope this makes sence, in my head it does... At least. ;-)

Hannes Camitz - 4 years, 10 months ago

Good explanation!

philip wesel - 1 year, 3 months ago

engineer wrote this question

nadav hacmun - 2 years, 3 months ago

A cyclist moves with your bike straight

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