# Confusion about conservation of linear momentum in a bike

A bike is moving with some velocity.There is some frictional force between the wheels of bike and ground.Now you apply brakes and the bike stops after some time.Brakes apply a force say F on wheels which slows down rotation of wheels,and finally wheels stop rotating.According to newtons 3rd law,wheels will also exert a force of equal magnitude on brakes (in the opposite direction of the force F).Thus,this reaction force on brakes gives momentum to bike (and this momentum is equal in magnitude to the loss of momentum due to slowing down rotation of wheels). Thus,momentum is conserved so bike would not lose its velocity but rotation of wheels is slowing down continuously.In that case,to obey the law of conservation of momentum, the bike would start sliding and sliding will be opposed by frictional force(between the wheels of bike and ground).This frictional force is the reason of losing momentum.My question is- is this possible that the reaction force on brakes gives momentum to bike (and this momentum is equal in magnitude to the loss of momentum due to slowing down rotation of wheels)? All suggestions are welcome.

• Well you are not considering losses due to heat generation on brakes and the heat lost to ground due to friction. – harshit54 Nov 17 '18 at 13:25
• The law of conservation of momentum is only valid when no external forces act on the system. In this case, there is a brake force and a force due to friction so conservation laws are not valid. – harshit54 Nov 17 '18 at 13:28