Question

Why do a wheel Balance when it is in motion and it falls when kept at rest?

Answer 1

Centrifugal force counteracting the gravitational force, makes the flat, circular object (i.e., a coin) stay up while in motion, and it falls flat when in rest.

Answer 2

where the pseudovectors τ and L are, respectively, the torque on the gyroscope and its angular momentum, the scalar I is its moment of inertia, the vector ω is its angular velocity, and the vector α is its angular acceleration.
It follows from this that a torque τ applied perpendicular to the axis of rotation, and therefore perpendicular to L, results in a rotation about an axis perpendicular to both τ and L. This motion is called precession. The angular velocity of precession ΩP is given by the cross product:



Precession on a gyroscope
Precession can be demonstrated by placing a spinning gyroscope with its axis horizontal and supported loosely (frictionless toward precession) at one end. Instead of falling, as might be expected, the gyroscope appears to defy gravity by remaining with its axis horizontal, when the other end of the axis is left unsupported and the free end of the axis slowly describes a circle in a horizontal plane, the resulting precession turning. This effect is explained by the above equations. The torque on the gyroscope is supplied by a couple of forces: gravity acting downward on the device's centre of mass, and an equal force acting upward to support one end of the device. The rotation resulting from this torque is not downward, as might be intuitively expected, causing the device to fall, but perpendicular to both the gravitational torque (horizontal and perpendicular to the axis of rotation) and the axis of rotation (horizontal and outwards from the point of support), i.e., about a vertical axis, causing the device to rotate slowly about the supporting point.
Under a constant torque of magnitude τ, the gyroscope's speed of precession ΩP is inversely proportional to L, the magnitude of its angular momentum:

where θ is the angle between the vectors ΩP and L. Thus, if the gyroscope's spin slows down (for example, due to friction), its angular momentum decreases and so the rate of precession increases. This continues until the device is unable to rotate fast enough to support its own weight, when it stops precessing and falls off its support, mostly because friction against precession cause another precession that goes to cause the fall.
By convention, these three vectors - torque, spin, and precession - are all oriented with respect to each other according to the right-hand rule.
To easily ascertain the direction of gyro effect, simply remember that a rolling wheel tends, when it leans to the side, to turn in the direction of the lean