Introduction

The Laws of Motion were given by Isaac Newton. These laws explain the relationship between the motion of an object and the forces acting on it.

1. Newton’s First Law of Motion (Law of Inertia)

Statement

An object remains at rest or continues to move with uniform velocity in a straight line unless acted upon by an external unbalanced force.

Key Concept: Inertia

• Inertia is the tendency of an object to resist changes in its state of motion.
• Greater mass ⇒ greater inertia.

Types of Inertia

1. Inertia of Rest
2. Inertia of Motion
3. Inertia of Direction

Examples

• Passengers fall backward when a bus starts suddenly.
• Dust comes out when a carpet is beaten.
• A coin drops into a glass when the card beneath it is flicked.

2. Newton’s Second Law of Motion

Statement

The rate of change of momentum of an object is directly proportional to the applied force and occurs in the direction of the force.

Formula

$F = ma$

Where:

• $F$ = Force (Newton)
• $m$ = Mass (kg)
• $a$ = Acceleration (m/s²)
  
  

  Where:

  • $p$ = Momentum
  • $m$ = Mass
  • $v$ = Velocity

  SI Unit of Force

  • Newton (N)

  Important Points

  • Force produces acceleration.
  • Acceleration is directly proportional to force.
  • Acceleration is inversely proportional to mass.

  Examples

  • A football moves farther than a stone when kicked with the same force.
  • Empty carts accelerate more easily than loaded carts.

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  3. Newton’s Third Law of Motion

  Statement

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

  Formula

  $F_{AB} = -F_{BA}$

  Examples

  • Recoil of a gun
  • Rocket propulsion
  • Walking on the ground
  • Swimming

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  Conservation of Momentum

  Statement

  In an isolated system, the total momentum remains constant if no external force acts.

  Formula

  $m_1u_1 + m_2u_2 = m_1v_1 + m_2v_2$

  Where:

  • $u$ = Initial velocity
  • $v$ = Final velocity

  Applications

  • Rocket motion
  • Collision problems
  • Explosion phenomena
    
    
    
    
    
    
    

Frictional Force

• Opposes relative motion.
• Depends on surface nature.

Types

• Static friction
• Kinetic friction
• Rolling friction

3. Normal Reaction Force

• Force exerted by a surface perpendicular to it.

Free Body Diagram (FBD)

A Free Body Diagram represents all external forces acting on an object.

Steps to Draw FBD

1. Isolate the object.
2. Draw all external forces.
3. Mark directions clearly.

Applications of Laws of Motion

• Vehicle motion
• Sports
• Rocket launching
• Lifting objects
• Walking and running
• Machine design

Important Units

Quick Revision Points

• First Law → Defines force and inertia.
• Second Law → Gives magnitude of force.
• Third Law → Explains interaction forces.
• Momentum is conserved in isolated systems.
• Force changes the state of motion. 

Introduction

The Stern–Gerlach experiment was performed in 1922 by Otto Stern and Walther Gerlach.
It demonstrated the quantization of angular momentum and provided evidence for the existence of electron spin.

Objective of the Experiment

The experiment was designed to study:

• The magnetic behavior of atoms
• Space quantization
• Angular momentum quantization

Basic Principle

When atoms having a magnetic moment pass through a non-uniform magnetic field, they experience a force.

The force depends on the orientation of the magnetic moment.

Experimental Setup

Apparatus Used

1. Oven producing silver atoms
2. Collimator to make a narrow beam
3. Non-uniform magnetic field
4. Detection screen/plate

Working

• Silver atoms are heated in an oven.
• A narrow atomic beam is formed.
• The beam passes through a strong non-uniform magnetic field.
• The atoms are deflected and strike the detector screen.

Expected Classical Result

According to classical physics:

• Magnetic moments could have any orientation.
• Therefore, the beam should spread continuously on the screen.

Actual Observation

Instead of a continuous band:

• The beam split into two distinct spots.

This showed that:

• Only two orientations were allowed.
• Angular momentum is quantized.

Mathematical Concept

The magnetic force on an atom is:

$F = \mu_z \frac{dB}{dz}$

Where:

• $F$ = Magnetic force
• $\mu_z$ = Magnetic moment component along z-axis
• $\frac{dB}{dz}$ = Magnetic field gradient

Spin Quantization

For electrons:

$m_s = \pm \frac{1}{2}$

Thus only two spin orientations exist:

• Spin up $(+\frac{1}{2})$
• Spin down $(-\frac{1}{2})$

This caused the beam to split into two parts.

Why Silver Atoms Were Used

Silver atoms contain:

• One unpaired electron in the outer shell

Hence:

• Net magnetic moment is non-zero
• Easier to observe splitting

Significance of the Experiment

The Stern–Gerlach experiment:

• Proved space quantization
• Supported quantum theory
• Demonstrated electron spin
• Contradicted classical physics predictions
• Became the foundation of quantum mechanics

Applications

1. Quantum Mechanics

Used to explain spin states and angular momentum.

2. Magnetic Resonance

Important in:

• MRI
• NMR spectroscopy

3. Particle Physics

Used in spin analysis of particles.

4. Quantum Computing

Spin states act as quantum bits (qubits).

Key Results

Limitations

• Works effectively for atoms with magnetic moments
• Requires strong non-uniform magnetic fields

Important Terms

Quick Revision

• Conducted by Stern and Gerlach in 1922.
• Silver atom beam used.
• Beam split into two parts.
• Proved quantization of spin.
• Important evidence for quantum mechanics.