# Newtons 2nd law and longitudibal dynamics of bicycle

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?

• So cycle moves due to friction & you don't impart external force, right???? – user36790 Feb 16 '15 at 16:45
• 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. – user36790 Feb 16 '15 at 16:52
• I was about to write it. I really don't think static friction will act in different directions; both 'll act forward. – user36790 Feb 16 '15 at 17:03