is the rate at which something called the "vector potential", A, is changing. The electric field becomes:Ĭ in the added term is the speed of light. When electric charges are in motion - that is, when electric currents are present - the electric field has to be modified to include a term that takes account of the motion of the charges. This relationship, however, is only true for "static" electric fields: fields produced by electric charges that are all at rest and stay that way. Formally this looks like:Į is the electric field strength, the gradient "operator", and is the electric potential. You may remember from an undergraduate course in electricity and magnetism that the electric field of an electric charge can be represented by something called a "scalar potential" - a "function" that assigns a single number to each point in space so that when the "gradient" of the function (the spatial rate of change of the function) is computed you get back the electric field strength (a vector quantity with magnitude and direction). ) The full-blown argument is rather formal and a bit daunting, but it's easy to see that gravity causes inertia in a simple little argument modeled on that presented by Sciama back in 1953. Raine back in the very early 1980s: Reports of Progress in Physics, 44, 1151-1195.
It turns out, as a matter of fact, that this is true in general relativity theory, but it took a while to show this. Back in 1953 Dennis Sciama showed that gravity could account for inertial reaction forces as long as the interaction of local stuff with the gravity field of distant matter was like the interaction of electric charges and currents with the electromagnetic field. The cause of inertial reaction forces has been understood to be the action of gravity for quite some time now. It's thought by some folks these days that the cause of inertial reaction forces isn't yet really understood, or that they have just succeeded in figuring out the explanation for these forces in terms of their new theory. from O then since all the particles have the same angular velocity (the body is rigid).THE ORIGIN OF INERTIA THE ORIGIN OF INERTIA and are distributed at distances r 1, r 2, r 3, etc. It follows that the kinetic energy of the whole body is the sum of the kinetic energy of its component particles. If v 1 is its linear velocity along the tangent to the path, at the instant shown then v 1= r 1ω and the kinetic energy of A=(1/2) m 1 v 1 2=(1/2) m 1 v 1 2ω 2 A particle A of mass m, at a distance r 1 from O describes its own circular path. Suppose the body is rotating about an axis through O with a constant angular velocity ω. We shall find out by considering the kinetic energy of the rotating body Kinetic Energy of a Rotating Body Similarly, the person on the swivel chair, has a greater moment of inertia when their arms are outstretched than when there hands are close to their body.
The greater is its measure of moment of inertia.Įxperiment shows that a wheel with most of its mass in the rim is more difficult to start or stop. The more difficult it is to change the angular velocity of a body about a particular axis. For rotational motion, the coresponding property is called moment of inertia. The mass of a body is a measure of its built-in opposition to any change in linear motion. The angular velocity of the system is clearly dependent on how the mass is distributed about the axis of rotation.
When he extends his hands the speed of rotation decreases but increases when he brings them closer to his body. This may be shown by someone who is sitting on a freely rotating stool with a heavy weight in each hand. The way in which the mass of the body is distributed then effects its behaviour. When this is not realistic we have to regard the rotating body as a system of conserved 'particles' moving in circles of different radii. In the cases considered so far we have treated the body as a particle so that 'all of it' revolves in a circle of the same radius.
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