Units 1, 2, 3, 4, and 5: Motion, Forces, Moments, Springs, and Pressure

perhaps the simplest concepts to master, these topics will be vital for everything to come.

remember, all the formulae that you need are in the formulae page.

this is the fundemental relationship describing motion: speed = distance/time.

now here is a disance time graph, where the gradient describes the speed. this makes sense mathematically as the gradient is change in y/change in x.

Now, a speed-time graph is little more complicated. the gradient now represents acceleration, or the change in velocity over time

The total area under the graph is the displacement, which means the distance travelled.

Now onto force. Force connects to motion through the equation F=ma. (force = mass * acceleration)

Here are the the key points to remember about force:

Newtons three laws. the 1st law can be remembered as the law of inertia. the 2nd law is simply f=ma. the third law is every action has an equal and opposite reaction.

You will also have to draw free body diagrams, or force diagrams.

These are simple. However, some people have trouble with using two forces to calculate a resultant force. Just remember that forces act the same way as vectors in maths. The questions you get in IGCSE are simple. You can solve them by using a scale drawing or pythagoras.

Take this for example. the resultant force is 10N because 10^2 = 6^2+8^2

For scale drawings, set a scale and make sure you write the scale on the paper. Normally, you should use a scale of 1N = 1cm. Just draw the forces according to the scale, and link them up, then measure the length of the resultant force. Make sure to use a ruler.

An important question that will apear in almost every single exam is terminal velocity. You have to know how to describe the changes in resultant force and how it affects acceleration and velocity.

Also familarise yourself with the graph:

Force can also be defined as the rate of change of momentum.

F = P/T where P is impulse and T is time. impulse is simply the change in momentum.

To recap momentum is mass*velocity, unit kgms.

Momentum is always conserved. Take this classic example of two metal balls hitting each other:

For these types of problems, simply calculate the sum of momentum using the masses and velocities of the balls before the collision and make sure the total momentum after the collision remains the same.

A question that doesn’t appear very often but is still good to know is centripetal force. refer to the image below:

it is important to remember that the accleration and velocity of the object is constantly changing. This is because they are vector quantities and when their direction changes, they change.

Finally, let us talk about weight and gravity. Weight is simply mass*gravity. However, weight is measured in newtons instead of kilograms.

Gravity is what caused an apple to fall on Newton.

Gravity on earth is 9.8m/s^2. Gravity is simply a force that causes acceleration towards the center of the celestial object. Gravity is different on different planets.

Gravity is much more complicated and interesting, but that is all you need to know about it for IGCSE. Look at General Relativity if you want to learn more.

A bit about turning effects/moments:

so basically, increasing force or distance from pivot increases moment of a force.

Equilibrium: equilibrium (balance) is achieved under two conditions:

no resultant force (Fnet = 0)

clockwise moment = anticlockwise moment (no turning effect)

Force also cause stretching in elastic objects.

Springs stretch proportionally to the force applied on them until it reaches the limit of proportionality.

Spring Constant K = Force/Extension. The bigger the spring constant, the harder it is to stretch the spring. After the limit of proportionality, the spring is deformed and it usually stretches more for the same force applied.

Pressure is also caused by the exertion of force.

Pressure = Force/Area

In fluids, due to the weight of the liquid or gas, pressure = density*gravity*height

That's it for now. It is important to note that I have omitted certain details to make this as concise and helpful as possible. If there is something I have not covered here, please leave a comment on the forums.