Newton’s laws of motion: force, mass, acceleration, connected particles

What is Force?

Force is a push or pull that can change the motion of an object. Think of a skateboard: the push from your foot is a force that starts the skateboard moving. ⚡️

Key symbols: $F$ for force, $m$ for mass, $a$ for acceleration.

Newton’s First Law – The Law of Inertia

Objects stay at rest or keep moving in a straight line unless a force acts on them.

• Example: A soccer ball on the field stays still until someone kicks it.
• Analogy: A book on a table stays put until you lift it.

Newton’s Second Law – The Force Equation

$$F = ma$$

This means the force applied to an object is equal to its mass times its acceleration.

To find acceleration: $a = \dfrac{F}{m}$

Newton’s Third Law – Action & Reaction

For every action, there is an equal and opposite reaction.

• Example: When you jump, your feet push down on the ground (action) and the ground pushes you up (reaction).
• Analogy: Two ice skaters pushing off each other to glide apart.

Connected Particles – Tension & Masses

When two masses are linked by a string, they share the same acceleration.

Diagram (text only):

  Mass 1 (m1) ----|---- Mass 2 (m2)
  Tension (T) acts on both
  

Equations:

• For mass 1: $T = m_1 a$
• For mass 2: $T = m_2 a$
• Since both have the same $a$, we can solve for $a$ using the total mass: $a = \dfrac{F_{\text{total}}}{m_1 + m_2}$

Exam Tips 📚

• Always identify the forces acting on each object.
• Use free‑body diagrams. Draw arrows for forces and label them.
• Check units: Force (N), Mass (kg), Acceleration (m/s²).
• Remember: $F = ma$ is the core equation for most problems.
• When dealing with connected particles, consider the system as a whole first, then split into individual parts.

Quick Practice Problem

A 4 kg cart is pulled by a 12 N force. What is its acceleration?

1. Write the equation: $F = ma$
2. Plug in the values: $12 = 4a$
3. Solve for $a$: $a = 3\,\text{m/s}^2$

Answer: 3 m/s²

Common Mistake Alert ⚠️

Don’t forget to use the correct sign for forces. If a force acts to the right, it’s positive; to the left, negative.

Also, do not mix up mass and weight. Weight is a force ($mg$), while mass is a measure of matter.