No real advance in metaphysics can take place, and natural science itself is in some danger, until the true history of the evidences of the laws of mechanical force is restored; and then it will soon appear that in the force of collision what we know is not material points determining one another's opposite accelerations, but bodies by force of impenetrable pressure causing one another to keep apart.
The Galileo-Newton theory of motion is that, relative to a suitably chosen base, and with suitable assignments of mass, all accelerations of particles are made up of mutual (so-called) actions between pairs of particles, whereby the two particles forming a pair have accelerations in opposite directions in the line joining them, of magnitudes inversely proportional to their masses.
The total acceleration of any particle is that obtained by the superposition of the component accelerations derived from its association with the other particles of the system severally in accordance with this law.
It is defined by the property that relative to it all accelerations of particles correspond to forces.
These are needed only so far as they introduce differences of accelerations of the several particles.
If u be the acceleration at unit distance, the component accelerations parallel to axes of x and y through 0 as origin will be ux, uy, whence ~ = ~sy.
It is sometimes convenient to resolve the accelerations in directions having a more intrinsic relation to the path.
Where p is the radius of curvature of the path at P, the tangential and normal accelerations are also expressed by v dv/ds and v1/p, respectively.
The component accelerations at P in these directions are therefore du do dir /dO\f dv do idfdO\ .14
These expression~ therefore give the tangential and normal accelerations of P; cf.
The directions of the radial and tangential accelerations of the point B are always known when the position of the link is assigned, since these are to be drawn respectively parallel to and at right angles to the link itself.
In applying this principle to the drawing of an acceleration diagram for a mechanism, the velocity diagram of the mechanism must be first drawn in order to afford the means of calculating the several radial accelerations of the links.
* To find the force competent to produce the instantaneous acceleration of any link of a meclianism.In many practical problems it is necessary to know the magnitude and position of the forces acting to produce the accelerations of the several links of a mechanism.
When the link forms part of a mechanism the respective accelerations of two points in the link can be determined by means of the velocity and acceleration diagrams described in 82, it being understood that the motion of one link in the mechanism is prescribed, for instance, in the steam-engines mechanism that the crank shall revolve uniformly.
It is to be noticed that only the directions of the accelerations of two points are required to find the point Z.