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Why is easier to hold your balance on a moving bicycle than when it's not in motion ?



Let's take the easiest case when the pedals are not moving.

The centripetal force provided by moving Tyre's of bicycle balances your weight. Hence more the motion more easy to hold the balance
This is true in part to the fact that the moments of balance required are weak when moving. The slower that bicycle goes the more balance is required because as things slow down more balance is required. The moment of least balance required is when you are moving in a straight upright line, it is as if the effort to create balance is non existent. Consider a motorcycle moving down the road, very little balance is required as you point the cycle in the forward straight direction. Make a turn however and balance and control of speed and line are required. Come to a full stop and you had better put two feet down to maintain balance or you will have a 4 to 5 hundred pound machine on the ground. Hope this helps without all the biophysics attached.
You may know well that unless we apply a force (it may even be friction) it is not possible to stop a moving body moving along a straight line.

Newton鈥檚 law states that all object will be in uniform motion till a force acts on it.

The same law holds good for rotational motion also.

In the case of a rotational motion, a wheel rotating in its axis will be rotating with uniform angular speed until a torque acts on it.
The direction of the axis maintains its direction.

In the case of the cycle wheels, the axes of rotation of the wheels are horizontal when in motion.

The wheels keep their angular speed as well as the direction of the axis always constant unless some external torque is applied.

Till a torque acts on them, they keep their axis in a horizontal position.

In the case of slow speeds the torque needed is small and friction and other small forces produce this torque and hence the cycle falls to the ground.

When you stop pedaling, friction slows down the speed of rotation of the wheels and when sufficiently slowed down small torques make it fall.

If the speed is maintained then the axis will also maintain its direction.

A top maintains its rotation about a vertical axis when speed is large. To make it to topple greater torque is necessary when the speed is relatively high.

If there is no friction, a top will be rotating for ever about its axis, even for slow speeds.
Balance is possible on a bicycle because the line of force through the forks meets the ground behind the front wheel. Provided the bicycle is in motion, the effect of this is that it automatically steers out of a tilt. You can see this by holding a bike at rest - tilt it right and the front wheel will turn left, out of the tilt. Of course this only works when the bike is moving.

Angular momentum and gyroscopic effects are entirely negligible - if they were not, you would not be able to turn a corner.
You are not 'holding your balance' when the bike is moving. Example: The bike starts to fall over to the left. You turn the front wheel to the left. The side load of the road on the tire moves the bottom of the wheel to the left, bringing it under the CG of the bike and restoring 'balance'.
In actual practice this is happening continuously and you are unaware of it. The steering geometry causes the front wheel to turn the correct way to restore balance. This explains the ability to ride a bike 'no hands'
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