Question

Need a simple explanation as to how gyroscope precession occur in a  spinning wheel which is held up by one end of its axle.

Answer 1

How gyroscope precession occur in a spinning wheel which is held up by one end of its axle.

A spinning wheel which is held up by one end of its axle will precess in the sense shown if it has that direction of spin.

If the spin is reversed, then it will precess in the opposite direction. The sense of precession is determined by the direction of torque due to the weight of a spinning wheel. That torque is perpendicular to the angular momentum of a wheel.

We know that, precession is a change in the orientation of rotational axis of a rotating body.

The top precesses around a vertical axis, since the torque is always horizontal and perpendicular to the angular momentum.

If the top is not spinning, then it acquires angular momentum in a direction of the torque and it rotates around a horizontal axis which falling over just as we would expect.

# Mathematically, we can solve & get a precession angular velocity (_P) :

= r M g sin

Thus, we have

dL = (r M g sin ) dt

The angle by the top precesses through in time (dt) is given by -

d = dL / L sin

d = (r M g sin ) dt / (L sin )

d = (r M g / L) dt

(d / dt) = (r M g) / L

_P = (r M g) / L                                                                     { Since, L = I }

_P = r M g / I

where, r = distance from the pivot to center of mass of the gyroscope

M = mass of wheel

g = acceleration due to gravity

I = moment of inertia of the gyroscope’s spinning wheel

= angular frequency of the gyroscope wheel

In this derivation, the precession angular velocity is much less than the angular velocity of gyroscope wheel.