Editing Precession (section)

===Classical (Newtonian)===

[[File:PrecessionOfATop.svg|thumb|right|256px|The [[torque]] caused by the normal force – {{math|'''F'''<sub>g</sub>}} and the weight of the top causes a change in the [[angular momentum]] {{math|'''L'''}} in the direction of that torque. This causes the top to precess.]]

Precession is the change of [[angular velocity]] and [[angular momentum]] produced by a torque. The general equation that relates the torque to the rate of change of angular momentum is:
<math display="block">\boldsymbol{\tau} = \frac{\mathrm{d}\mathbf{L}}{\mathrm{d}t}</math>
where <math>\boldsymbol{\tau}</math> and <math>\mathbf{L}</math> are the torque and angular momentum vectors respectively.

Due to the way the torque vectors are defined, it is a vector that is perpendicular to the plane of the forces that create it. Thus it may be seen that the angular momentum vector will change perpendicular to those forces. Depending on how the forces are created, they will often rotate with the angular momentum vector, and then circular precession is created.

Under these circumstances the angular velocity of precession is given by: <ref>{{cite book |last1=Moebs |first1=William |last2=Ling |first2=Samuel J. |last3=Sanny |first3=Jeff |title=11.4 Precession of a Gyroscope - University Physics Volume 1 {{!}} OpenStax |date=Sep 19, 2016 |location=Houston, Texas |url=https://openstax.org/books/university-physics-volume-1/pages/11-4-precession-of-a-gyroscope |access-date=23 October 2020 |language=en}}</ref>

:<math>\boldsymbol\omega_\mathrm{p} = \frac{\ mgr}{I_\mathrm{s}\boldsymbol\omega_\mathrm{s}} = \frac{ \tau}{I_\mathrm{s}\boldsymbol\omega_\mathrm{s}\sin(\theta)}</math>

where {{math|''I''<sub>s</sub>}} is the [[moment of inertia]], {{math|'''''ω'''''<sub>s</sub>}} is the angular velocity of spin about the spin axis, {{mvar|m}} is the mass, {{math|''g''}} is the acceleration due to gravity, {{mvar|θ}} is the angle between the spin axis and the axis of precession and {{math|''r''}} is the distance between the center of mass and the pivot.  The torque vector originates at the center of mass. Using {{math|1='''''ω''''' = {{sfrac|2π|''T''}}}}, we find that the [[Frequency|period]] of precession is given by:<ref>{{cite book |last1=Moebs |first1=William |last2=Ling |first2=Samuel J. |last3=Sanny |first3=Jeff |title=11.4 Precession of a Gyroscope - University Physics Volume 1 {{!}} OpenStax |date=Sep 19, 2016 |location=Houston, Texas |url=https://openstax.org/books/university-physics-volume-1/pages/11-4-precession-of-a-gyroscope |access-date=23 October 2020 |language=en}}</ref>
<math display="block">T_\mathrm{p} = \frac{4\pi^2 I_\mathrm{s}}{\ mgrT_\mathrm{s}} = \frac{4\pi^2 I_\mathrm{s}\sin(\theta)}{\ \tau T_\mathrm{s}}</math>

Where {{math|''I''<sub>s</sub>}} is the [[moment of inertia]], {{math|''T''<sub>s</sub>}} is the period of spin about the spin axis, and {{mvar|'''τ'''}} is the [[torque]]<!-- Torque is not introduced -->. In general, the problem is more complicated than this, however.