Ask a Scientist: Forces give rise to motion

Otago Daily Times, 21 November 2014

Peter Keyzers, of Upper Hutt, asked:-

Why is it that all matter in the universe is subject to a spinning motion? Both at the micro and macro level, bodies spin around their own axis as well as around other bodies. What is responsible for all this spinning, and is this maybe the universal force that makes the universe possible?

David Wiltshire, a physicist at the University of Canterbury responded:

Spinning is not a universal force, but a general property of particles moving in response to any force that "conserves angular momentum".

This conservation law holds for any force which acts on two objects with a strength that depends on intrinsic properties of objects (such as mass or charge) and on the distance between the two objects, but not on any other relational quantity such as their relative velocity. Both the two long range forces of nature, gravity and electromagnetism, have a strength that decreases in proportion to the square of the distance, and so are of this type. That is why the phenomenon of things spinning is so universal in nature.

If you think of the simple case of the circular motion of a planet about the Sun, then the force on the planet is always the same strength as its distance from the Sun does not change. The force always acts in the direction perpendicular to the instantaneous motion of the planet, no work is being done. The planet is in a state of perpetual equilibrium characterized by two physical quantities -- its total energy and angular momentum -- staying the same. Linear momentum is the product of mass and velocity, where velocity is the rate of change of distance. For circular motion the magnitude of the distance is not changing, but the angle in the orbit is continually changing which is why angular momentum is the relevant concept.

Of course, there can be many motions other than circles - for a planet or comet in Newtonian mechanics there are ellipses, parabolae and hyperbolae as well. But all of these orbits have the property that if you were to calculate the product of the mass, speed and radial distance of the orbiting body from the Sun then you will always end up with the same number -- the angular momentum -- which does not change. A comet will speed up as it approaches the Sun, so that even though the distance to Sun is smaller, the product of the distance and speed is constant (so long its mass stays the same and is not evaporated away in a close encounter).

For things that rotate on their axes, the same principle applies. An ice skater who pirouettes on a frictionless surface will spin faster if she pulls her arms in, or slower as she moves them out, in such a way that the product of her component masses, their speeds and distances from the axis of her rotation stay the same number.

It's a general property of physics that if things can happen, they will happen. The fundamental forces of nature, including gravity and electromagnetism, give rise to motions that conserve angular momentum and total energy. Spinning motions are allowed by such laws; so they are the things that happen.

Professor David Wiltshire
Department of Physics and Astronomy
University of Canterbury