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When a bicycle (of gross vehicle mass $m$) accelerates ($a$) forward, such that both the wheels are in pure rolling (no slipping), then: static friction ($f_{s1}$) acts on the front wheel backwards, static friction ($f_{s2}$) acts on the rear wheel forward, rolling friction ($f_{r1} \& f_{r2}$) acts on both the wheels backwards. Thus, $$m.a = f_{s1} - f_{s2} - f_{r1} - f_{r2}$$

Am I correct?

My main doubt is whether the static friction force on the front wheel acts backward or not?

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  • $\begingroup$ So cycle moves due to friction & you don't impart external force, right???? $\endgroup$ – user36790 Feb 16 '15 at 16:45
  • $\begingroup$ Yes that's right. Think of the car. Its tyres push the road backward; the road exerts frictional force to the car forward thus moving it. This doesn't mean it is providing energy to the car from the road; the energy is emanating from the engine. $\endgroup$ – user36790 Feb 16 '15 at 16:52
  • $\begingroup$ I was about to write it. I really don't think static friction will act in different directions; both 'll act forward. $\endgroup$ – user36790 Feb 16 '15 at 17:03
  • $\begingroup$ There is no rolling friction really. Static friction acts to keep the wheels from slipping. $\endgroup$ – John Alexiou Jan 2 '20 at 22:37
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Taking it to be a conventional bicycle, we notice that it has a rear wheel drive.So you apply torque on the rear wheel by means of pedalling, which tends to rotate it .At the point of contact between road and the rear bicycle tire , the impeding motion tire wrt the road is in backward direction. The frictional force acts in forward direction at the rear wheel through the COM that is at its centre which produces the translational force which helps us to advance a bicycle in forward direction.Now, the front wheel possessing no torque, tends to slide or drag on the road, now the impending motion of the point of contact of front wheel and road surface is in forward direction(wrt road ) so the friction there acts in backward direction at the point of contact of the road and the tire which provides the essential torque for it to rotate. So summing it up, the friction on fore wheels act in backward directions while that on rear wheel is in forward direction.

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