Reduct Blog

I never liked the equation F = ma, since it confuses cause with effect in the physical context we usually refer to, i.e. bodies moving in space. We look at a body, moving in space, and try to change its motion, i.e. effect an acceleration. The more force we apply, the greater the resulting acceleration, a ∝ F, (all else being equal). The more massive the body, the less the resulting acceleration, a ∝ 1/ m, (all else being equal). So, F / m = a, is a better description, at least to me. (Newton's words in the Principia were ~ "The change of motion is proportional to the motive force, and is made in the direction of the straight line in which that force is impressed".)

Great question, and one that I struggled with while trying to understand the meaning of momentum. The best explanation I have found, for what the product of two magnitudes is, comes from Robert Knapp's "Mathematics is About the World" He also tackles the case of adding 4 apples to 3 oranges ( 7 "fruits"), and multiplying "umbrellas by bananas" (as per that hilarious article title that michel123456 linked to): So, to answer your specific question as to what a "kilogram-meter", I would say that it is a type of unit, a compound unit that is composed of kilograms and meters (obviously enough). And in fact, this unit (or rather "kilogram-kilometers") is used in the freight industry, as part of a rate like "CO2 emitted per kilogram-kilometer". Visually, this is hard to imagine I suppose, but I see a kilogram weight sliding along a meter stick, to represent a sort of dynamic unit, one which can be used to compare the movement of arbitrary kilograms of freight over whatever distance. When you move a kilogram a meter, you see only the kilogram and the meter distance, but there is an indirect magnitude here, something resulting indirectly from that movement of the kilogram that distance. Once we consider the amount of time taken for that kilogram to move that meter, then we have momentum. It's like the kilowatt-hour, which results from letting a kilowatt device run for an hour. The kilowatt-hour is exactly like the kilogram-meter, in that the first unit (kW or kg) is "run" over the second unit (hour or m), and we create a new, indirect, derived "third" unit (kw·h or kg·m) : in the case of the kilowatt-hour, this compound unit is a unit of energy. (I don't know enough physics to know what a kilogram-meter measures, but it doesn't seem too far from energy to me -- although my concept of "energy" is rather vague) I'll be tackling multipart rates and compound units over the coming months over at my blog, which is against the rules to advertise as part of a discussion thread, so feel free to check it out.