Welcome to Mechanics!
Welcome to the first step in your Mechanics journey! Before we start calculating how fast a car zooms or how high a ball bounces, we need to speak the same "language." In physics and maths, that language is made of quantities (the thing we measure) and units (how we measure it).
Don't worry if this seems a bit "sciencey" at first—mechanics is just the maths of how things move in the real world. By the end of these notes, you’ll be a pro at using the standard building blocks of the universe.
1. The "Big Three": Fundamental Quantities
In the SI system (the international standard), there are three basic building blocks we use in AS Mechanics. Think of these like the primary colors—you can't make them from anything else, but you can combine them to make every other "color" (quantity) in the world.
Mass
What it is: The amount of "stuff" or matter in an object.
SI Unit: Kilogram (\(kg\)).
Wait, why not grams? In everyday life, we use grams for baking, but in Mechanics, the kilogram is our standard.
Common Mistake: Always check your question! If a mass is given in grams (\(g\)), you must divide by 1000 to turn it into \(kg\) before doing any math.
Length
What it is: The distance between two points.
SI Unit: Metre (\(m\)).
In your exams, you might see kilometers (\(km\)) or centimeters (\(cm\)). Always convert these back to metres first. 1 kilometre = 1000 metres.
Time
What it is: How long a duration lasts.
SI Unit: Second (\(s\)).
Quick Tip: If a problem mentions minutes or hours, convert them to seconds immediately!
Example: 2 minutes = 120 seconds.
Quick Review: The Fundamental Units
- Mass: Kilograms (\(kg\))
- Length: Metres (\(m\))
- Time: Seconds (\(s\))
2. Building Blocks: Derived Quantities
Now for the fun part! When we mix the "Big Three" together using multiplication or division, we get derived quantities. These describe more complex ideas like how fast something moves or how hard you push it.
Velocity and Speed
The Idea: Velocity is just "distance divided by time."
The Unit: Metres per second, written as \(ms^{-1}\) (or \(m/s\)).
Analogy: If you walk 2 metres every single second, your velocity is \(2 \, ms^{-1}\).
Acceleration
The Idea: This is the rate at which your velocity changes. If you are speeding up, you are accelerating.
The Unit: Metres per second squared, written as \(ms^{-2}\).
Did you know? Gravity on Earth pulls everything down with an acceleration of approximately \(9.8 \, ms^{-2}\). This is a number you will see a lot in this course!
Force
The Idea: A push or a pull. We calculate force by multiplying Mass \(\times\) Acceleration.
The Unit: Newton (\(N\)).
Deep Dive: One Newton is actually a combination of our base units. Since \(Force = mass \times acceleration\), then:
\(1 \, N = 1 \, kg \times 1 \, ms^{-2}\).
So, \(1 \, N = 1 \, kg\,m\,s^{-2}\).
Weight
The Idea: Weight is a specific type of Force. It is the force of gravity pulling on your mass.
The Formula: \(Weight = mass \times g\) (where \(g \approx 9.8 \, ms^{-2}\)).
The Unit: Because weight is a force, its unit is also the Newton (\(N\)).
Key Takeaway
Velocity uses \(m\) and \(s\). Acceleration uses \(m\) and \(s^{2}\). Force (and Weight) uses \(kg\), \(m\), and \(s^{2}\).
3. Mass vs. Weight: Don't Get Caught Out!
This is the most common area where students lose marks. In everyday speech, we use "mass" and "weight" as the same thing, but in Mechanics, they are very different!
Mass is constant. If you go to the Moon, your mass stays the same because you are still made of the same amount of "stuff." It is measured in \(kg\).
Weight changes. On the Moon, gravity is weaker, so you would weigh less. It is a force measured in \(N\).
Memory Trick:
Mass is Matter (stays the same).
Weight is a Working Force (changes with gravity).
4. Working with Units: A Step-by-Step Guide
When you sit down to solve a Mechanics problem, follow these steps to make sure your units are correct:
- Identify the quantities: Read the question and underline the numbers. Is it a mass? A distance? A time?
- Check for "Impostor" units: Are there any grams (\(g\)), kilometres (\(km\)), or hours (\(h\))?
- Convert to SI:
- \(km \rightarrow m\) (Multiply by 1000)
- \(g \rightarrow kg\) (Divide by 1000)
- \(minutes \rightarrow seconds\) (Multiply by 60)
- Calculate: Plug your "clean" SI numbers into your formulas.
- Label the answer: Always put the correct unit (e.g., \(N\), \(ms^{-1}\)) at the end of your answer!
Final Summary Table
Keep this table handy while you practice!
Quantity | Symbol | SI Unit | Unit Symbol
Length | \(s\) or \(d\) | metre | \(m\)
Time | \(t\) | second | \(s\)
Mass | \(m\) | kilogram | \(kg\)
Velocity | \(v\) or \(u\) | metres per second | \(ms^{-1}\)
Acceleration | \(a\) | metres per second squared | \(ms^{-2}\)
Force / Weight | \(F\) or \(W\) | Newton | \(N\)
Quick Review Box:
Remember, Mechanics is all about consistency. If you use \(kg\), \(m\), and \(s\) for everything, your final answer will naturally come out in the correct SI unit! If you start mixing in grams or centimetres, the math will break. Always convert first!