Physics | Force and Newton’s laws

Force and Newton's Laws of Motion

Hello everyone! Welcome to your study notes on Force and Newton's Laws. This is one of the most important topics in all of Physics! Why? Because it explains why things move (or stay still). From a football soaring into the air to the planets orbiting the sun, the ideas we'll cover here are the rules of the game for motion in our universe.

Don't worry if this seems tricky at first. We'll break everything down into simple, easy-to-understand parts with lots of real-world examples. Let's get started!

1. The Basics of Force

So, what exactly is a force?

• A force is simply a push or a pull on an object.
• Forces can make an object start moving, stop moving, change direction, or change its shape.
• Force is a vector quantity. This is super important! It means a force always has both a magnitude (how strong it is) and a direction (which way it's pushing or pulling).
• The unit we use to measure force is the Newton, and its symbol is N.

For example: When you kick a football, your foot applies a force to the ball (a push). Gravity applies a force that pulls the ball back to the ground (a pull).

Key Takeaway

A force is a push or a pull, measured in Newtons (N). It's a vector, so direction matters!

2. Adding and Resolving Forces

Often, more than one force acts on an object at the same time. The total combined force is called the net force or resultant force. Finding the net force is key to understanding how the object will move.

Adding Forces

• Forces in the same direction: Just add them up! (e.g., Two people pushing a car forward).
• Forces in opposite directions: Subtract the smaller force from the larger one. The direction of the net force will be the same as the larger force. (e.g., A tug-of-war game).

Free-Body Diagrams: Your Best Friend in Physics!

A free-body diagram is a simple drawing that shows ALL the forces acting on a single object. It helps you see the situation clearly.

How to draw one (step-by-step):

1. Draw a simple box or dot to represent the object.
2. Identify all the forces acting ON the object (gravity, pushes, pulls, friction, etc.).
3. Draw an arrow for each force, starting from the box and pointing in the direction the force is acting.
4. Make the length of the arrow represent the size of the force (longer arrow = bigger force).
5. Label each arrow clearly (e.g., Weight, Friction, Push).

Example: A book resting on a table. The free-body diagram would have a dot, an arrow pointing down labelled "Weight (W)", and an equal-sized arrow pointing up labelled "Normal Reaction from table (R)".

Resolving Forces (Splitting them up!)

Sometimes a force acts at an angle. It's often easier to "split" this force into two parts that are perpendicular to each other (usually horizontal and vertical components). This is called resolving a force.

Think of it like this: if you pull a suitcase with a handle at an angle, part of your force is pulling it forward (horizontally) and part of it is pulling it up (vertically). Resolving the force helps us find out how much of your effort goes into each direction.

Key Takeaway

The net force is the overall force on an object. Use free-body diagrams to visualise all the forces, which makes solving problems much easier.

3. Newton's First Law: The Law of Inertia

Sir Isaac Newton came up with three amazing laws that describe motion. Here's the first one.

Newton's First Law states: An object will stay at rest or continue to move at a constant velocity (constant speed in a straight line) unless a net force acts on it.

This sounds complicated, but it's simple. It means things like to keep doing what they're already doing!

The Key Idea: Inertia

The tendency of an object to resist changes in its motion is called inertia.

• If an object is still, it wants to stay still.
• If an object is moving, it wants to keep moving in the same way.

Mass is a measure of an object's inertia. The more mass an object has, the more inertia it has, and the harder it is to change its motion.

Analogy: It's much harder to push-start a heavy truck (lots of mass and inertia) than it is to push a small toy car (very little mass and inertia).

A common force that stops things from moving forever is friction. Friction is a force that opposes motion or the tendency of motion between surfaces in contact.

What are Balanced Forces?

When the net force on an object is zero ($$F_{net} = 0$$), we say the forces are balanced. According to Newton's First Law, an object with balanced forces acting on it will either be:

1. Stationary (not moving).
2. Moving at a constant velocity.

Common Mistake Alert! Just because an object isn't moving doesn't mean there are no forces on it. It means all the forces are balanced and cancel each other out!

Key Takeaway

Inertia is resistance to change in motion. Mass measures inertia. If forces are balanced ($$F_{net}=0$$), an object's velocity does not change.

4. Newton's Second Law: Force, Mass, and Acceleration

This law tells us what happens when forces are unbalanced.

Newton's Second Law states: The acceleration of an object is directly proportional to the net force acting on it, and inversely proportional to its mass.

This leads to the most famous equation in Physics:

$$F_{net} = ma$$

Where:
• F_net is the net force acting on the object (in Newtons, N).
• m is the mass of the object (in kilograms, kg).
• a is the acceleration of the object (in metres per second squared, m/s²).

This means: • A bigger net force produces a bigger acceleration.
• For the same force, a bigger mass will have a smaller acceleration.

A Quick but Important Detour: Mass vs. Weight

People often mix these up, but in Physics, they are very different!

• Mass (m): The amount of 'stuff' in an object. It's a measure of inertia. It's a scalar and is measured in kg. Your mass is the same whether you are on Earth or on the Moon.
• Weight (W): The force of gravity acting on an object. It's a vector and is measured in N. Your weight would be much less on the Moon because the Moon's gravity is weaker.

We can calculate weight using Newton's Second Law! Weight is a force, and the acceleration is the acceleration due to gravity, g.

$$W = mg$$

On Earth, g is approximately 9.81 m/s².

Key Takeaway

When forces are unbalanced, the object accelerates. The relationship is $$F_{net} = ma$$. Remember that mass is how much stuff is in you (kg), and weight is the force of gravity on you (N).

5. Newton's Third Law: Action and Reaction

This law describes a fundamental property of all forces.

Newton's Third Law states: For every action, there is an equal and opposite reaction.

This means that forces always come in pairs. If object A pushes on object B, then object B pushes back on object A with a force that is equal in magnitude and opposite in direction.

These pairs of forces are called an action-reaction pair.

Examples:
• Walking: Your foot pushes backward on the ground (action). The ground pushes forward on your foot (reaction), which moves you forward.
• A Rocket: The rocket pushes hot gas downwards (action). The hot gas pushes the rocket upwards (reaction).
• You sitting on a chair: Your body pushes down on the chair (action). The chair pushes up on your body (reaction).

Common Mistake Alert! Why don't action-reaction forces cancel each other out? Because they act on DIFFERENT objects! To see if an object moves, you only look at the forces acting ON IT (like in a free-body diagram).

Key Takeaway

Forces always come in pairs. The action and reaction forces are equal in size, opposite in direction, and act on different objects.

6. Moments: The Turning Effect of a Force

Sometimes, a force can cause an object to turn or rotate. Think about opening a door. You push on the handle, and the door rotates around its hinges. This turning effect is called a moment (or torque).

The point an object rotates around is called the pivot (or fulcrum).

The size of the moment depends on two things:
1. The size of the force.
2. The perpendicular distance from the pivot to the force.

The formula is:

$$ \text{Moment} = \text{Force} \times \text{Perpendicular distance from pivot} $$

The unit for a moment is the Newton-metre (Nm).

Real-world example: It's easier to open a heavy door by pushing far from the hinges (large distance) than by pushing near the hinges (small distance). You create a larger moment for the same amount of force!

The Principle of Moments & Equilibrium

For an object to be balanced and not rotating (like a balanced seesaw), the total clockwise moments must equal the total anticlockwise moments.

$$ \sum \text{Clockwise Moments} = \sum \text{Anticlockwise Moments} $$

For an object to be in total equilibrium (not moving and not rotating), two conditions must be met:

1. The net force must be zero.
2. The net moment about any pivot must be zero.

Centre of Gravity (CG)

The centre of gravity is the single point where the entire weight of an object can be considered to act.

• For a symmetrical object like a ruler, the CG is at its geometric centre.
• An object is stable as long as the vertical line passing through its CG falls within its base of support. A lower CG generally leads to greater stability. (Think of a low-slung racing car vs a tall bus).

Key Takeaway

A moment is the turning effect of a force ($$M = Fd$$). For an object to be balanced, total clockwise moments must equal total anticlockwise moments.