Newton’s first law of motion tells us that a particle in motion if unacted upon by force, will move continuously in a straight line without change of velocity.
Let A0, Fig. [60], be the position of the particle at any moment. Let A1 be its position after the time t; A2 be the position at the time 2t; A3 be the position at the time 3t, and so on.
Then the first law of motion tells us that the distances A0 A1, A1 A2, A2 A3, A3 A4, must form parts of the same straight line and must be all equal.
If lines O A0, O A1, O A2, etc., be drawn from any fixed point 0, then the areas of the triangles O A0 A1, O A1 A2, O A2 A3, 0 A3 A4, will be all equal. For each area is one-half the product of the base of the triangle into the perpendicular O T from O on A0 A1, and, as the bases of all the triangles are equal, it follows that their areas are equal.
Thus we learn that a particle moving without the action of force will describe around any fixed point O equal areas in equal times.
Fig. 60.—First Law of Motion exemplifies
Constant Moment of Momentum.
The product of the mass of the particle and its velocity is termed the momentum. If the momentum be multiplied by O T the product is termed the moment of momentum around O. We have in this case the simplest example of the important principle known as the conservation of moment of momentum.
The moment of momentum of a system of particles moving in a plane is defined to be the excess of the sum of the moments of momentum of those particles which tend round O in one direction, over the sum of the moments of momentum of those particles which tend round O in the opposite direction.
If we deem those moments in one direction round O as positive, and those in the other direction as negative, then we may say that the moment of momentum of a system of particles moving in a plane is the algebraical sum of the several moments of momentum of each of the particles.