An elementary treatise on kinematics and dynamics / by James Gordon MacGregor.

  • MacGregor James Gordon, 1852-1913.
Date:
1902
Catalogue details

Licence: In copyright

Credit: An elementary treatise on kinematics and dynamics / by James Gordon MacGregor. Source: Wellcome Collection.

Provider: This material has been provided by the Royal College of Physicians of Edinburgh. The original may be consulted at the Royal College of Physicians of Edinburgh.

    48/550 (page 30)
    [56 merit. Whether mean or instantaneous, uniform or variable, they are quotients of a certain speed by a certain time. If a be the value of the rate of change, v that of the speed, and t that of the time, we have ■a = v/t. If then v and t are both unity, a must be unity also. Hence we have taken as our unit of rate of change •of speed that of a point whose speed is changing at the rate of unit of speed per unit of time. The English unit of the foot-second system is thus 1 ft.-per-sec. per sec; that of the mile-hour system, 1 ml.-per-hour per hour. Similarly, the French unit of the cm.-sec. system is 1 om.-per-sec. per sec. The second per second is often •omitted; but this shortened mode of specifying the unit is apt to be misleading. 57. Dimensions of Rate of Change of Speed.—We have seen (56) that a = v/t. If now [A] denote the magnitude of the unit of rate of change of speed, [V] and [T] those of the units of speed and of time respec- tively, we have (15) a x l/[A]; v x 1/[F]; t oc 1/[T]. Hence [A] oc [V]/[T]. But (47) [V] cc Hence [A] oc [L]/[Tf, or [A] oc [L}[T}-\ i.e., the magnitude of the unit of rate of change of speed is directly proportional to the magnitude of the unit of length, and inversely proportional to the square of the magnitude of the unit of time. 58. As in the case of speed (48), so also in that of rate of change of speed, it may be shown that, if [A], [L], and [T] are the magnitudes of the units of one derived system, and [A'], [L'], [T'] those of another similarly derived system, [A]/[A'] = [L]/[L']^[TY/[TJ: