In a typical circuit breaker, upon release of the restraining latch the movable-contact arm will begin to accelerate. The dynamic behavior of the movable arm is determined by the effective mass of the arm, the strength and preloading of the drive spring, the magnitude of the current through the contacts, frictional forces on the arm hinge and arm travel, and the speed and detailed action of the latch release mechanism.
Since the current flow is constricted and forced to flow in converging paths to contact spots on both bulk contact faces, as shown in Figure 5.1, there will be components of current flow which are anti-parallel to each other within the adjoining contacts.
These anti-parallel components form single-turn “loop” inductors. These inductors tend to expand in an effort to minimize their self-inductance, and thus minimize their stored magnetic energy. The magnetic force which acts to expand the current loop inductors is then a net repulsion force between the two bulk contacts. Holm [5.1], Snowdon [5.2] and a number of others,
have shown that the repulsion force due to the current constriction in a single contact spot is approximately given by 
where i is the magnitude of the instantaneous current through the contact spot, a is the effective radius of the single contact spot, and A is the effective radius of the total bulk contact surface area. This force of electromagnetic repulsion adds to any mechanical forces which tend to separate the contacts. By itself, it is generally small in comparison to the movable contact spring force, except under high current conditions. At high currents the repulsion force (due to the current squared term in Equation 5.3) can become significant, even dominant, in certain structures [5.3].
This repulsion force has even been utilized in the construction of a mechanical AC fault current limiter [5.3]. In this device, movable contact arms, are restrained together by a spring mechanism (see Figure 5.2a). 
Under very high fault current levels the electromagnetic repulsion between the contact arms overcomes the restraining springs and forces the contacts apart. Figure 5.2b illustrates that the resulting arcis longer than that needed in a normal AC breaker. It thus has a very high arc voltage, which “bucks” the fault current drive voltage, and limits the peak fault current to values less than that which would flow without the arc voltage in series with the faulted circuit.
The mechanical dynamics of the parting of circuit breaker contacts are very similar to the dynamics of the armature of a magnetic circuit breaker. Barkan [Equations 5.4, 5.5 and 5.6] has presented detailed studies of contact dynamics for large, electric utility type breakers. The theory of small light duty breakers, however, is very similar.
Figure 5.3 shows a simplified contact mechanism.
This figure is an adaptation of Barkan’s Figure 2 given in reference [5.4]. Barkan obtained closed form solutions for the system shown in Figure 5.3 for the following situations: (a) ideal system, lumped concentrated masses, no drag forces, negligible electromagnetic force, and instantaneous latch release; (b) as in (a) but with a finite latch release time; (c) as in (a) but with viscous drag proportional to the square of the moving contact velocity; (d) as in (a) but with distributed but rigid contact linkages; and (e) as in (a) but with distributed flexible contact linkages. We will restrict our interest to only cases (a) and (b).
For an ideal system, case (a), we have for the equation of motion for the movable contact
where m is the equivalent mass of the movable contact (including the contact arm), x is the contact position measured from complete contact closure, k is the drive spring constant, and xs is an equivalent position which is proportional to the initial force on the contact immediately after latch release. If the latch releases instantaneously at time = 0, we have for the solutions of (5.4)
where ω is the angular velocity 
v(t) is the contact velocity, xo is the initial contact position ( = 0 at start) and vo is the initial contact velocity ( = 0 at start).
If the latch does not release the contact instantaneously then the initial forcing term in (5.4) must be modified. From strain gauge measurements during latch release Barkan [5.4] found that a latch restraining force drops off approximately as a cubic time function. Thus, the equation of motion becomes
where T is the time required for the latch to completely release the contact arm. The solutions to (5.7), valid for 0<t<T and zero initial position and velocity are given by
and
For t > T we can use (5.6) and (5.7), with initial conditions given by (5.8) and (5.9) evaluated at t=T, and with time t given by t—T.
We plot the contact position x, normalized to the equivalent initial force position Xs, for both instantaneous and non-instantaneous latch release in Figure5.4.
In this plot we have assumed that the non-instantaneous release is completed in two tenths of the spring-mass cycle time, that is, ωT/2π = 0.2. The corresponding contact velocity plots for these cases normalized to ωxs, are given in Figure 5.5 the movable contact “average” velocity vav
Also normalized to ωxs. Typical measured values for average velocities for small circuit breaker structures are 20-300 cm/sec.
If the movable contact is not on a spring loaded arm, but rather on a flexible snapaction bi-metal structure, the simple equation of motion, Equation 5.4, does not apply. The actual dynamics of a snapping structure are quite complex, but the end result, a co-sinusoidal (in time) like movement is quite similar to that of a simple spring loaded arm. 
Figure 5.6 is a plot of the measured displacement of a contact on a snap-action low power toggle switch [5.7]. The solid line is the measured result taken from a high speed film. The dashed line is an empirical fit of the data to an equation of the form
Where xss is the steady state separation (1.1mm), α= 208 sec-1, n = 1.45 and ω is the radian mechanical frequency. For this structure the average velocity at x =͂ 1.0 mm is seen to be
