Chapter-04 , Laws Of Motion

Chapter 4: Laws of Motion – Class 11 Physics Notes 

• In the last chapter, we studied motion using velocity and acceleration.
  
  

• Now we ask: What causes motion?
  
  

Daily life experience:

• A football moves only when we kick it.
  
  

• A stone goes up only when we throw it.
  
  

• Wind makes branches move.
  
  

• A boat moves with river flow.
  👉 So, it looks like force is needed to start or stop motion.

• Motion of any object is controlled by forces.
  
  

• Before Newton, people believed force is needed to keep a body in motion (Aristotle’s idea).
  
  

• Newton explained the real relation between force and motion through his three laws of motion.

Force is not always needed for motion.

• If no external force acts, a body at rest stays at rest, and a moving body continues to move in a straight line.
  
  

• This property is called inertia.
  
  

Newton’s three laws give us the rules:

• First Law → Explains inertia (why motion or rest continues).
  
  

• Second Law → Defines force as the cause of change in momentum.
  
  

• Third Law → Explains action–reaction pair of forces.

⚖️ Force 

Force is a push or pull on an object.

📌 Formula:

F = m × a
(Force = mass × acceleration)

📌 Example: Kicking a ball applies force.

Types of Forces 

Contact Force                                                                                      Push, Pull, Friction

Non-contact Force                                                                          Gravity, Magnetism

📜 Newton’s Laws of Motion 

1️⃣ First Law – Law of Inertia

“An object remains at rest or in uniform motion unless acted upon by an external force.”

📌 Also called the Law of Inertia.

📌 Example: A book on a table stays still until pushed.

2️⃣ Second Law – Force and Acceleration

“Force is equal to the rate of change of momentum.”

👉 F = m × a

📌 More mass = More force needed
📌 Example: It’s harder to push a heavy box than a light one.

3️⃣ Third Law – Action-Reaction

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

📌 Example: You jump → ground pushes you up.

🧊 Inertia

Inertia = Natural tendency of an object to resist change in motion.

Inertia is the property of an object to resist any change in its state of motion or rest. 

📌 It depends on mass.

👉 More mass = More inertia 

📌 Types:

• Inertia of Rest

👉 Tendency of an object to stay at rest unless something moves it.

📌 Example: A book stays on a table unless you push it.

• Inertia of Motion

👉 Tendency of an object to stay in motion unless something stops or changes its speed.

📌 Example: A moving car keeps going even after you turn off the engine (until friction or brakes stop it).

• Inertia of Direction

👉 Tendency of an object to keep moving in the same direction unless a force changes its direction.

📌 Example: When a car takes a sharp turn, you feel thrown to one side.

🔹 What is Linear Momentum? 

Linear Momentum is the quantity of motion an object has. It is the product of mass and velocity.

📌 Formula:

p = m × v

Where:

• p = momentum
  
  

• m = mass (kg)
  
  

• v = velocity (m/s)

✅ Vector Form of Linear Momentum 

📐 Dimensional Formula of Momentum

To find the dimensional formula:

p = m × v
Mass = [M], Velocity = [L T⁻¹]

📌 Dimensional formula = [M L T⁻¹]

🔄 Variation of Momentum 

📊 Case 1: Equal Masses, Different Velocities 

📊 Case 2: Different Masses, Equal Velocities 

📊 Case 3: Different Masses, Different Velocities 

🔍 Derivation: Measurement of Force from Newton’s 2nd Law 

📘 Newton’s Second Law in Component Form 

💥 Impulse 

📘 What is Impulse?

Impulse is the effect of a force acting for a short time on a body.

🧠 Definition:
Impulse is the product of force and the time duration for which it acts.

🔁 Relation with Momentum (Impulse-Momentum Theorem)

From Newton's Second Law:

✅ Impulse = Change in momentum 

📏 SI Unit of Impulse:

• Ns (newton-second)
  
  

• Also: kg·m/s (same as momentum)
  
  

🎯 Important Points:

• Impulse is a vector quantity.
  
  

• If a large force acts for a short time, impulse can still be significant.
  
  

• Common in sports, collisions, etc.
  
  

📈 Force-Time Graph:

• The area under the Force–Time graph gives impulse.

📘 What Happens When Force is Not Constant?

When a variable force acts on a body, we cannot use the simple formula:

because F vector changes with time.
In such cases, we calculate impulse using integration or the area under the force-time graph.

📈 Force–Time Graph (Area = Impulse)

The area under the Force–Time graph gives impulse:

• Positive area = positive impulse
  
  

• Negative area = negative impulse (force acts in opposite direction)
  
  

📌 If the force is changing (e.g., triangular or curved shape), use the total area under the curve to find impulse.

Newton’s Third Law of Motion 

“To every action, there is an equal and opposite reaction.” 

This means:

• Forces always occur in pairs.
  
  

• If body A applies a force on body B, then body B applies an equal and opposite force on body A.

✅ Both forces:

• Act on different objects
  
  

• Are equal in magnitude
  
  

• Are opposite in direction
  
  

• Occur at the same time

Law of Conservation of Momentum 

Statement of Law:

“In a closed system with no external force, the total momentum remains constant.”

That means:

Total initial momentum   =  Total final momentum

Derivation of Law of Conservation of Momentum from Newton’s Third Law 

Equilibrium of a Particle 

A particle is said to be in equilibrium when the net external force acting on it is zero. 

🔁 Types of Equilibrium:

1. Static Equilibrium
   
   

   • The particle is at rest and remains at rest.
     
     

   • Example: A book resting on a table.
     
     

2. Dynamic Equilibrium
   
   

   • The particle is moving with constant velocity (zero acceleration).
     
     

   • Example: A car moving at constant speed on a straight road.
     
     

Friction and Its Types 

⚙️ What is Friction?

Friction is a force that opposes the relative motion (or tendency of motion) between two surfaces in contact.

It acts parallel to the surface and opposite to the direction of motion or applied force.

Coefficient of Friction (μ)

• A unitless constant that depends on the nature of surfaces in contact.
  
  

• Two types:

Angle of Friction 

What is Angle of Friction?

The angle of friction is the angle between the normal reaction force and the resultant of normal force and limiting friction.

It tells how steep a surface can be before an object starts sliding.

Angle of Repose

The angle of repose is the minimum angle of an inclined plane at which a body just begins to slide down due to gravity, without any external force. 

Derivation of Relation Between θ and φ ( angle of friction & angle of repose )

Consider a block of mass m placed on a rough inclined plane at angle ϕ (angle of repose).

The object just begins to slide: