Welcome to Space, Time, and Motion!
In this chapter, we are going to look at the rules that govern how everything in the universe moves. Whether it’s a football flying through the air or a planet orbiting a star, the same basic principles of Physics apply. By the end of these notes, you’ll be able to predict where an object will land, how much energy it has, and what happens when things crash into each other. Don’t worry if some of the math looks intimidating at first—we’ll break it down into simple steps!
1. Scalars and Vectors: Direction Matters
In Physics, some numbers just tell us "how much," while others tell us "how much and in which direction."
- Scalars: These only have magnitude (size). Examples: mass, energy, time, and speed.
- Vectors: These have magnitude AND direction. Examples: displacement, velocity, acceleration, force, and momentum.
Adding and Resolving Vectors
When you have two vectors (like two people pushing a box), you can't always just add the numbers together. You have to consider the angles.
Adding Vectors: If two vectors are at right angles, use Pythagoras: \( a^2 + b^2 = c^2 \). To find the angle, use trigonometry: \( \tan \theta = \frac{opposite}{adjacent} \).
Resolving Vectors: This is like "un-adding" a vector. You break a diagonal force into a horizontal part (\( F_x \)) and a vertical part (\( F_y \)).
- Horizontal component: \( F_x = F \cos \theta \)
- Vertical component: \( F_y = F \sin \sin \theta \)
Memory Aid: Use SOH CAH TOA to remember your trig! Also, remember that Cosine is for the component Close to the angle (\( \cos \theta \)).
Quick Review: Scalars vs. Vectors
A scalar is like your age (no direction), whereas a vector is like a GPS instruction ("Walk 50 meters North").
2. Describing Motion: The Language of Graphs
We use graphs to tell the story of an object’s journey. There are two main types you need to master:
Displacement-Time Graphs
- The slope (gradient) represents the velocity.
- A flat line means the object is stationary.
- A straight diagonal line means constant velocity.
Velocity-Time Graphs
- The slope (gradient) represents the acceleration.
- The area underneath the line represents the displacement (how far it moved).
- A flat line means constant velocity (zero acceleration).
Common Mistake: Don't confuse distance with displacement. Distance is the total ground covered; displacement is how far you are from your starting point in a straight line!
3. The Equations of Motion (SUVAT)
When an object is moving with constant acceleration, we use the SUVAT equations. The letters stand for:
- \( s \): displacement
- \( u \): initial velocity
- \( v \): final velocity
- \( a \): acceleration
- \( t \): time
The core equations you need to use are:
\( v = u + at \)
\( s = ut + \frac{1}{2} at^2 \)
\( v^2 = u^2 + 2as \)
\( s = \frac{(u + v)}{2} \times t \)
How to solve SUVAT problems:
- Write down the values you know (you usually need three).
- Identify the value you want to find.
- Pick the equation that has those four variables in it.
- Rearrange and solve!
Did you know? All objects in free-fall (with no air resistance) accelerate downwards at approximately \( 9.81 m/s^2 \) regardless of their mass!
4. Newton’s Laws of Motion
Isaac Newton gave us three rules that describe how forces cause motion.
Newton’s First Law (Inertia)
An object will stay still or keep moving at a constant speed in a straight line unless a resultant force acts on it.
Analogy: A hockey puck on perfectly smooth ice will slide forever until it hits the wall.
Newton’s Second Law (\( F = ma \))
Force equals mass times acceleration. This means the harder you push something, the faster it accelerates; but the heavier it is, the harder you have to push.
Equation: \( F = ma \)
Also defined as the rate of change of momentum: \( F = \frac{\Delta (mv)}{\Delta t} \)
Newton’s Third Law (Action and Reaction)
If Object A exerts a force on Object B, then Object B exerts an equal and opposite force of the same type on Object A.
Example: When you lean against a wall, the wall pushes back on you with the exact same force.
5. Energy, Work, and Power
Energy cannot be created or destroyed—it only changes from one form to another. This is the Principle of Conservation of Energy.
Work Done (\( \Delta E \))
Work is done whenever a force moves an object. If the force is at an angle \( \theta \) to the direction of motion:
\( \Delta E = F \Delta s \cos \theta \)
Kinetic and Potential Energy
- Kinetic Energy (KE): The energy of movement. \( KE = \frac{1}{2} mv^2 \)
- Gravitational Potential Energy (GPE): The energy an object has because of its height. \( GPE = mgh \)
Power
Power is how fast energy is being transferred. It's measured in Watts (W).
\( Power = \frac{\Delta E}{t} \)
When an object is moving at a constant velocity \( v \) against a constant force \( F \):
\( Power = Fv \)
6. Momentum and Impulse
Momentum (\( p \)) is "mass in motion." Every moving object has it.
\( p = mv \)
Conservation of Momentum
In any collision or explosion, the total momentum before equals the total momentum after (as long as no outside forces act on the system).
Impulse
Impulse is the change in momentum. It is calculated by multiplying the force by the time it acts for: \( Impulse = F \Delta t \).
Example: Airbags in cars work by increasing the time of the impact, which reduces the force felt by the passenger.
Key Takeaway: Momentum
If a 1kg ball moving at 2m/s hits a stationary 1kg ball, the first ball stops and the second one moves off at 2m/s. The "motion" is simply passed along!
Summary of "Understanding Processes" in Motion
Moving through this chapter is about connecting these ideas. Forces cause acceleration (Newton's 2nd Law), which changes velocity (SUVAT), which changes the energy and momentum of the system. Master the graphs and the vectors first, and the rest of the math will start to feel like a puzzle where you just need to find the right piece!