S-Cool Revision Summary

S-Cool Revision Summary

Vectors Versus Scalars

Vectors and scalars are two types of measurements you can make.

  • A scalar measurement only records the magnitude (or amount) of whatever you are measuring.
  • A vector measurement records the magnitude of the thing you are measuring and the direction.

Vector Addition

Adding scalars is easy because you can just add the numbers.

For Example: 3kg + 4 kg = 7 kg

Adding vectors needs much more care. You have to take into account their magnitude and direction.

For Example: What's 3N + 4N? Well, it depends on the directions! Look at the possibilities...

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or

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Note: 1N is not balanced

or

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So in other words, you add vectors geometrically (using geometry). You should be able to do this using accurate diagrams (don't forget your protractor) or by using Pythagoras.

Resultant Vectors

The resultant vector is the one that you get when you add two or more vectors together. It is a single vector that has the same effect as all the others put together. Finding the resultant vector when the forces are in different directions can be tricky if you don't like Pythagoras, so here's a couple to get you going!

Worked Example:

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Using Pythagoras: R2 = 82 + 72

So, R = √113 = 10.6 N

Resolving Vectors into Components

We have just shown that any two vectors can be represented by a single resultant vector that has the same effect. Guess what?! You can do the same thing in reverse! Any single vector can be represented by two other vectors (components), which would have the same effect as the original one:

Resolving Vectors into Components

You need to use trigonometry to find the two components of a vector. Remember the two components will always be at right angles.

Resolving Vectors into Components

Check that you understand how to calculate the values of the components.

Speed and Velocity

Both speed and velocity tell us how far something is travelling in unit time. As velocity is a vector it must also tell us what direction the object is travelling in.

Speed (m/s) =
distance moved (m)

time taken (s)
Velocity (m/s) =
displacement change (m)

time taken (s)

Acceleration

Acceleration tells us how rapidly something is changing speed - for instance, the change in speed in unit time. Deceleration is the same thing, but we give it a negative sign as the speed will be decreasing.

Acceleration (m/s2) =
Change in velocity (m/s)

time taken (s)

Displacement-time graphs

These show the motion of an object very clearly and allow you to find position and velocity at any time. Any graph that you see will be a combination of these sections.

The Basics of Linear Motion

Notice that the gradient =
Change in D

Change in t
= the velocity at any time.

When the velocity is changing, as on the lower two graphs, you can find the velocity at any point by drawing a tangent touching the graph at that point by drawing a tangent touching the graph at that point and working out its gradient using the same equation.

Velocity-time graphs

These fare similar to displacement-time graphs, but this time velocity is on the y-axis. Here are the only possibilities that you'll come across at A-level.

The Basics of Linear Motion

Notice that the gradient =
Change in velocity

Change in time
= acceleration or deceleration.

You also need to know that the area under the line gives you the displacement of the object up to that point.

Acceleration-time graphs

Note: All three of the movement graphs are related to each other as the:

  • Gradient of D/t graph gives you the points on the v/t graph.
  • Gradient of v/t graph gives you the points on the a/t graph.