Force
Forces and Motion | Energy and Thermal Physics

Momentum is a vector

Teaching Guidance for 14-16 Supporting Physics Teaching

Shown by an arrow

Wrong Track: Momentum is a simple measure of the motion, like the energy in the kinetic store, and so it's just a bigger or smaller number, except that the number can sometimes be negative.

Right Lines: p has to be shown with an arrow. It's a quantity with a direction, just like v. Just like in mathematics, you need ordered sets of numbers to show these quantities, as they're vectors (in our world, we'd need three such numbers to cover the three dimensions up-down, left-right, and in-out).

Thinking about the learning

Momenta met in traditional problems often feel just like numbers on a number-line, because only one dimension is considered in order to simplify the problem. So it's perhaps not surprising that the vector nature of momentum is hard to get hold of from the traditional examples, where momentum is represented as either a positive or a negative number.

Thinking about the teaching

The SPT materials have been using arrows to show quantities with direction throughout. Regular use of these kinds of depictions can emphasise that the relative magnitudes don't capture all that there is to say about the quantity: directions are also important. It might pay to occasionally use such arrows in two or three dimensions, because always working in one (so effectively using only signed quantities) tends to obscure the vector nature of momentum.

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