What's the best measure of the quantity of motion in an object?
Charlie stands on a station and the full London bound through train rushes past. Alice, sitting on the London-bound train, notices Charlie as she stares out of the window of the carriage, and also, shortly afterwards, sees Bob standing in the corridor of a local stopper-train making his way towards Birmingham. They're all
objects – the stopper-train containing Bob, the London-bound train seating Alice, and Charlie – of different masses and recorded as moving at different velocities by the three observers, Alice, Bob and Charlie.
But how much motion do they have? What's the best
quantity of motion – the best quantity with which to record just how much motion they have?
Is it best to measure how much motion there is, what it takes to get something moving, or what it takes to stop something that's already moving?
These kinds of questions occupied clever people for quite a while in the mid-1700s. The question is not straightforward.
What's the best measure of the quantity of motion in an object?isn't an easy question to answer. The debate between the protagonists raged long and often fiercely over the centuries that it took to evolve a powerful and useful description of motion.
Some argued for:
quantity of motion = mass × velocity2 and others for
quantity of motion = mass × velocity.
But most were agreed that the factors that increased the quantity of motion were:
- An increase in the mass.
- An increase in the velocity.
In this episode you'll look again at the energy in the kinetic store, to find out under what circumstances that is a useful measure of the quantity of motion.
quantity of motion = 12 × mass × velocity2
You'll also meet a new measure of motion (momentum), which turns out to be extremely useful in interactions, and therefore will be met again in episode 04.
quantity of motion = mass × velocity
Both have their place: you'll need to learn when each is useful, and therefore in which situations you might choose one rather than the other to help you get a handle on that situation and understand it. You'll often want to know what might happen next, and so the kinds of predictions that you can make from the given situations will be a major influence in deciding which you choose.