Question

Why a bicycle moving with constant velocity feels no frictional force?

Answer 1

Action-reaction Forces act through the rod connecting the wheels. The forces are such that the front wheel is pushed in the forward direction and as a reaction the back moving

When the Bicycle is peddled in constant speed:
For Rear Wheel:
1. There is Torque being applied on the back wheel.
2. This has to be compensated by the Torque between Friction and the backward force of reaction mentioned above.
3. We assume the rear wheel to roll so the point of contact is vertically downwards having net 0 velocity. Hence there is no net torque dueto the couple of weight and Normal Reaction.
3. So the Friction has to act in Forward direction.

When the Bicycle is de-accelerating.
For Front Wheel,
1. There is no net external Force on the bicycle so the Friction on the front wheel has to be equal and opposite to the friction on the rear wheel in; i.e. in Backward Direction.

When the Bicycle is not peddled or is de-accelerating:
For Rear Wheel:
There is a net Torque Slowing down the motion, So again Friction is acting in Forward direction. Rest of the points for back wheel almost the same,
For Front wheel,
Because there is a net decreasing force, Friction has to act backward but more than the one acting on rear wheel.

When Bicycle is accelerating,
If the rear wheel is rolling, the friction will still act forwards but the net Torque wont balance.
Friction on the Front wheel will be such as that the net friction will be in front direction propelling the cycle ahead but it will be in backward direction if the wheel has to have a rotational acceleration w/o slipping.