If we integrate with respect to I between fixed limits, we obtain the principles of linear and angular momentum in the form previously given, Hence, whichever form of postulate we adopt, we are led to the principles of linear and angular momentum, which form in fact the basis of all our subsequent work.
Since the conditions in the region PQ remain always the same, the momentum perpendicular to AB entering the region at Q is equal to the momentum perpendicular to AB leaving the region at P. But, since the motion at Q is along AB, there is no momentum there perpendicular to AB.
Consider a submarine boat or airship moving freely with the direction of the resultant momentum horizontal, and the axis at a slight inclination 0.
So that no angular momentum enters at B, and therefore on the whole none leaves at A.
Lord Kelvin was thereby induced to identify magnetic force with rotation, involving, therefore, angular momentum in the aether.
Read on to see how that momentum has built over time, and continues to build.
The first uprising momentum of the whale--modifying its direction as he struck the surface--involuntarily launched him along it, to a little distance from the centre of the destruction he had made; and with his back to it, he now lay for a moment slowly feeling with his flukes from side to side; and whenever a stray oar, bit of plank, the least chip or crumb of the boats touched his skin, his tail swiftly drew back, and came sideways smiting the sea.
If two masses m1, nil moving in the same straight line impinge, with the result that the velocities are changed from u1, u2, to ui, ui, then, since the impulses on the two bodies must be equal and opposite, the total momentum is unchanged, i.e.
But it has velocity U, and therefore momentum poU 2 is carried in.
In later memoirs Reynolds followed up this subject by proceeding to establish definitions of the velocity and the momentum and the energy at an element of volume of the molecular medium, with the precision necessary in order that the dynamical equations of the medium in bulk, based in the usual manner on these quantities alone, without directly considering thermal stresses, shall be strictly valid - a discussion in which the relation of ordinary molar mechanics to the more complete molecular theory is involved.