Scalars v Vectors

Scalars are numbers that have a magnitude (size), but we don’t mind what direction or orientation of this number. Like mass or volume or speed. The number (plus units of course) tells us all we need to know about it. If we have two scalars it’s easy to add them up, it’s as simple as 3kg + 5kg = 8kg.

Vectors on the other hand have both a magnitude and a direction. Examples of vectors are forces and velocities (note this is different from speed) and we need to know both the magnitude and the direction of the number. You can often tell when you’re being asked about vectors because there will be a picture showing you angles or directions.

To add vectors is a little more difficult. Imagine you’re the point of interest and you have two siblings, one hanging off each arm. It’s easy to know which direction they will pull you if they are opposite each other, as the stronger one will win. But once they start pulling at different angles it’s a little trickier.

The simplest way to work out the resultant, which is what you get when you add more than one vector together, is by drawing a scale model. Take all the vectors and draw them following on from each other (rather than all working from one point), with the correct angles. The resultant will be from the origin to the end of the last vector, which you can measure from the scale.

This can get a bit complicated though, and time consuming as well, so we can use a mathematical technique, and a little help from our calculator, to work it out a bit faster. It’s best to only use this one when the two vectors are at right angles to each other. (As an aside you also want to make sure your calculator is in the right mode, you should be using “deg” rather than “rad” and as a quick check, sin 30 should be 0.5)

Once we have these techniques sorted out we can also then change a single vector into components, which means doing the reverse calculation to split the force up into two separate parts. Normally this will be to find the forces in the x-direction and the y-direction, and it’s sometimes called resolving into the component parts.

So watch out for the difference between vectors and scalars and when it comes to the tricky business of adding vectors make sure you take the directions into account. I always find drawing a little model helps, whether I do it to scale (to measure off the drawing) or not.