Precession

Precession refers to the motion whereby the rotational axis of a rotating object revolves around a fixed axis. The motion of the object maps out the surface of a cone.

This occurs when the object experiences a torque, ,which means force does not act through the centre of mass of the object, but instead, acts at a distance away from it.

Torque is defined as the vector product between the perpendicular distance between the action and the centre of mass, r, and the magnitude of the force, F.

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Maths Prerequisites:

Vector Product
Spherical Polar Coordinates

When an external torque is applied to the object, it experiences a change in angular momentum in the direction of the torque, which causes the angular velocity vector to change direction, since angular momentum and angular velocity are related by

In spherical polar coordinates, the component of angular momentum in the direction of the torque is given by , and so the torque is

[1]

Therefore, the angular velocity, denoting the rate of precession, is

[2]

Not only does a magnetic field induce precession, as in the case with the protons in the MRI scanner, gravitational field also causes precession, the best-known example of precession is a spinning top toy.

Did you know...

The earth also precesses?

This is because the axis of the earth is tilted at an angle from the direction of the gravitational field. It takes 26,000 years for the earth to complete one cycle of precession. [3]

References:

[1] Signell P and Kovacs J.S, "Angular Momentum and Torque: Precession", Michigan State University, Michigan (2001)

[2] Ibid.

[3] "Astronomy 518: Astrometry Lecture", University of Arizona, Retrieved from http://ircamera.as.arizona.edu/Astr_518/ametry.pdf [Accessed: 24.02.19]