Class 11 Physics Notes Chapter 5 (Chapter 5) – Physics Part-II Book

Alright class, let's get straight into Chapter 5: Laws of Motion from your Physics Part-II book. This is a foundational chapter, absolutely crucial not just for your Class 11 exams but for almost any government exam with a science component, like NDA, various state PSCs, SSC, Railways, etc. Pay close attention as we break down the concepts.

Chapter 5: Laws of Motion - Detailed Notes for Government Exam Preparation

1. Introduction & Force

• Force: A push or pull that changes or tends to change:
  • The state of rest of an object.
  • The state of uniform motion of an object (i.e., changes velocity - speed or direction).
  • The shape or size of an object.
• Force is a vector quantity (has both magnitude and direction).
• Historical Context:
  • Aristotle's Fallacy: Believed an external force is necessary to keep an object moving. (Incorrect for uniform motion).
  • Galileo's Contribution: Through experiments with inclined planes, Galileo concluded that objects move with constant velocity if no net force acts on them. This led to the concept of inertia.

2. Inertia & Newton's First Law

• Inertia: The inherent property of a body by virtue of which it resists any change in its state of rest or of uniform motion along a straight line.
  • Inertia is not a force; it's a property.
  • Mass is the measure of inertia. A body with greater mass has greater inertia.
• Types of Inertia:
  • Inertia of Rest: Resistance to change from a state of rest. (Ex: Dust particles fly off a carpet when beaten; passenger jerks backward when a bus starts suddenly).
  • Inertia of Motion: Resistance to change from a state of uniform motion. (Ex: Passenger jerks forward when a moving bus stops suddenly; athlete runs a short distance after crossing the finish line).
  • Inertia of Direction: Resistance to change in the direction of motion. (Ex: Mud flying tangentially off a rotating wheel; sparks from a grinding wheel).
• Newton's First Law of Motion (Law of Inertia):
  • Statement: "Everybody continues in its state of rest or of uniform motion in a straight line unless compelled by some external force to act otherwise."
  • This law provides a qualitative definition of force (Force is that which changes the state of rest or uniform motion).
  • It also defines inertia.
  • Inertial Frame of Reference: A frame of reference in which Newton's first law holds true (i.e., a non-accelerating frame). Examples: Frame fixed to the ground (approximately), frame fixed to distant stars.
  • Non-Inertial Frame: An accelerating frame of reference where Newton's first law does not hold without introducing pseudo-forces. (Ex: A rotating frame, an accelerating car).

3. Momentum & Newton's Second Law

• Linear Momentum (p): The quantity of motion possessed by a body.
  • Defined as the product of mass (m) and velocity (v).
  • Formula: p = mv
  • It is a vector quantity, direction is the same as velocity.
  • SI Unit: kg m/s
  • Dimensional Formula: [MLT⁻¹]
• Newton's Second Law of Motion:
  • Statement: "The rate of change of linear momentum of a body is directly proportional to the external force applied on the body, and this change takes place in the direction of the applied force."
  • Mathematical Form: F ∝ dp/dt or F = k (dp/dt)
  • In SI and CGS systems, the constant of proportionality k is chosen as 1.
  • Therefore: F = dp/dt
  • If mass 'm' is constant: F = d(mv)/dt = m (dv/dt) = ma (where a is acceleration). This is the most commonly used form.
  • This law provides a quantitative definition of force (Measure of force).
  • Unit of Force:
    • SI Unit: Newton (N). 1 N = 1 kg m/s² (Force required to accelerate 1 kg mass by 1 m/s²).
    • CGS Unit: Dyne. 1 dyne = 1 g cm/s².
    • Relation: 1 N = 10⁵ dyne.
• Impulse (J):
  • The effect of a large force acting for a short duration.
  • Defined as the product of the average force (F_avg) and the time interval (Δt) for which it acts. J = F_avg * Δt
  • Impulse-Momentum Theorem: Impulse is equal to the change in linear momentum of the body. J = Δp = p_final - p_initial
  • Vector quantity, direction is the same as the change in momentum (or the force).
  • SI Unit: Ns or kg m/s (Same as momentum).
  • Examples: Hitting a ball with a bat, catching a ball (increasing time reduces force), shock absorbers.

4. Newton's Third Law of Motion

• Statement: "To every action, there is always an equal and opposite reaction."
• Key Points:
  • Action and reaction forces are equal in magnitude.
  • They act in opposite directions.
  • They act simultaneously.
  • They act on different bodies. (This is why they don't cancel each other out).
  • Mathematical Form: F_AB = - F_BA (Force on A by B is equal and opposite to force on B by A).
• Examples:
  • Walking: We push the ground backward (action), the ground pushes us forward (reaction).
  • Swimming: Swimmer pushes water backward (action), water pushes swimmer forward (reaction).
  • Rocket Propulsion: Hot gases expelled downwards (action), rocket moves upwards (reaction).
  • Recoil of a Gun: Bullet moves forward (action), gun moves backward (reaction).
  • Book on a table: Book exerts force (weight) downwards on the table (action), table exerts an equal upward normal force on the book (reaction).

5. Conservation of Linear Momentum

• Principle: "If the net external force acting on a system of bodies is zero, then the total linear momentum of the system remains constant (conserved)."
• Derivation: From Newton's Second Law, F_ext = dp/dt. If F_ext = 0, then dp/dt = 0, which implies p = constant.
• System: A collection of particles or bodies interacting with each other.
• Isolated System: A system on which no net external force acts.
• Formula for a system of two bodies: If F_ext = 0, then p_initial = p_final.
  m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂
  (Where u₁, u₂ are initial velocities and v₁, v₂ are final velocities).
• Applications: Collisions (elastic and inelastic), explosions, recoil of guns.

6. Equilibrium of a Particle

• Equilibrium: A state where the net external force acting on a particle (or body) is zero.
• Condition: ΣF = 0 (Vector sum of all forces is zero).
• If ΣF = 0, then acceleration a = 0. This means the particle is either:
  • At rest (Static Equilibrium)
  • Moving with constant velocity (Dynamic Equilibrium)
• Concurrent Forces: Forces whose lines of action pass through a common point.
• Lami's Theorem: For a particle in equilibrium under the action of three concurrent forces F₁, F₂, F₃:
  F₁ / sin α = F₂ / sin β = F₃ / sin γ
  (Where α is the angle opposite F₁, β opposite F₂, γ opposite F₃). Useful for solving problems with three forces.

7. Common Forces in Mechanics

• Weight (W): Gravitational force exerted by the Earth on an object. W = mg. Acts vertically downwards towards the center of the Earth.
• Normal Reaction (N or R): Contact force exerted by a surface on an object, acting perpendicular (normal) to the surface. It arises due to electromagnetic interactions at the atomic level, preventing penetration.
• Tension (T): The pulling force transmitted axially by means of a string, cable, chain, etc. Acts along the string, away from the object it's attached to. In ideal problems, strings are often assumed massless and inextensible.
• Friction (f): Force that opposes relative motion or the tendency of relative motion between surfaces in contact. It's a contact force acting parallel to the surfaces.
  • Static Friction (f_s): Opposes impending motion. It's a self-adjusting force. 0 ≤ f_s ≤ f_s(max).
  • Limiting Friction (f_s(max)): The maximum value of static friction, just before motion begins. f_s(max) = μ_s N, where μ_s is the coefficient of static friction (depends on the nature of surfaces).
  • Kinetic Friction (f_k): Opposes actual relative motion. It's approximately constant for moderate speeds. f_k = μ_k N, where μ_k is the coefficient of kinetic friction. Generally, μ_k < μ_s.
  • Rolling Friction: Resistance to motion when an object rolls on a surface. Much smaller than kinetic or static friction (μ_r << μ_k < μ_s).
  • Laws of Limiting Friction:
    1. Independent of the apparent area of contact.
    2. Proportional to the normal reaction (N).
    3. Depends on the nature and polish of the surfaces in contact.
    4. Kinetic friction is slightly less than limiting friction.
• Spring Force (F_s): Restoring force exerted by a stretched or compressed spring.
  • Hooke's Law: F_s = -kx, where k is the spring constant (stiffness) and x is the displacement from the equilibrium position. The negative sign indicates the force opposes the displacement.

8. Solving Problems Using Newton's Laws

• Steps:
  1. Identify the System: Choose the body or bodies of interest.
  2. Draw Free-Body Diagram (FBD): Isolate the body and draw all external forces acting on it. Represent the body as a point mass if appropriate.
  3. Choose Coordinate System: Select convenient perpendicular axes (often horizontal/vertical or parallel/perpendicular to an incline).
  4. Resolve Forces: Break down any forces not aligned with the axes into components along the chosen axes.
  5. Apply Newton's Second Law: Write equations ΣF_x = ma_x and ΣF_y = ma_y for each body. If in equilibrium, ΣF_x = 0 and ΣF_y = 0.
  6. Solve Equations: Solve the resulting system of equations for the unknowns (e.g., acceleration, tension, normal force).
• Common Scenarios:
  • Blocks connected by strings (over pulleys or on surfaces).
  • Objects on inclined planes (resolve weight into components).
  • Elevator problems (apparent weight changes due to acceleration: N = m(g+a) if accelerating up, N = m(g-a) if accelerating down).

9. Circular Motion (Brief Overview)

• An object moving in a circle at constant speed is still accelerating because its direction (and hence velocity) is constantly changing.
• This acceleration, called centripetal acceleration (a_c = v²/r), is directed towards the center of the circle.
• Centripetal Force (F_c): The net force required to produce centripetal acceleration. It must be directed towards the center. F_c = ma_c = mv²/r.
  • Important: Centripetal force is not a new type of force. It is the role played by one or more existing forces (like tension, friction, gravity, normal force) that provides the necessary inward pull.

Multiple Choice Questions (MCQs)

1. A passenger sitting in a bus moving at a constant speed observes a coin on the floor that is stationary relative to him. If the bus suddenly brakes hard, the coin will:
   a) Remain stationary relative to the passenger.
   b) Move forward relative to the passenger.
   c) Move backward relative to the passenger.
   d) Fly upwards.

2. Newton's second law of motion gives a measure of:
   a) Inertia
   b) Force
   c) Momentum
   d) Acceleration

3. A cricketer lowers his hands while catching a fast-moving ball. This action helps to:
   a) Increase the impulse.
   b) Decrease the change in momentum.
   c) Increase the time of impact, thereby reducing the force.
   d) Decrease the time of impact, thereby reducing the force.

4. Action and reaction forces mentioned in Newton's third law:
   a) Act on the same body.
   b) Act on different bodies.
   c) Can cancel each other out.
   d) Are always gravitational forces.

5. A bomb at rest explodes into two fragments of masses m₁ and m₂. The total momentum of the fragments immediately after the explosion is:
   a) (m₁ + m₂)v
   b) (m₁ - m₂)v
   c) Zero
   d) Dependent on the energy released.

6. The coefficient of static friction (μ_s) between two surfaces is generally:
   a) Less than the coefficient of kinetic friction (μ_k).
   b) Equal to the coefficient of kinetic friction (μ_k).
   c) Greater than the coefficient of kinetic friction (μ_k).
   d) Equal to zero.

7. A block of mass 'm' is placed on a smooth inclined plane of inclination θ. What is the component of its weight acting parallel to the incline?
   a) mg
   b) mg cos θ
   c) mg sin θ
   d) mg tan θ

8. A lift is moving upwards with an acceleration 'a'. The apparent weight of a person of mass 'm' inside the lift will be:
   a) mg
   b) m(g - a)
   c) m(g + a)
   d) Zero

9. The physical quantity which is conserved when a gun recoils after firing a bullet is:
   a) Kinetic Energy
   b) Potential Energy
   c) Linear Momentum
   d) Angular Momentum

10. A force F = (6i - 8j + 10k) N produces an acceleration of 1 m/s² in a body. The mass of the body is:
    a) 10 kg
    b) 10√2 kg
    c) 20 kg
    d) 2√10 kg

Answer Key for MCQs:

1. b) Move forward relative to the passenger (Due to inertia of motion).
2. b) Force (F = ma or F = dp/dt).
3. c) Increase the time of impact, thereby reducing the force (Impulse = FΔt = constant change in momentum. Increasing Δt decreases F).
4. b) Act on different bodies.
5. c) Zero (Initial momentum was zero, and momentum is conserved in the absence of external forces).
6. c) Greater than the coefficient of kinetic friction (μ_k).
7. c) mg sin θ
8. c) m(g + a) (Normal reaction N = mg + ma).
9. c) Linear Momentum (Assuming no external force acts on the gun-bullet system).
10. b) 10√2 kg (Magnitude of F = √(6² + (-8)² + 10²) = √(36 + 64 + 100) = √200 = 10√2 N. Since F = ma, m = F/a = (10√2 N) / (1 m/s²) = 10√2 kg).

Study these notes thoroughly. Focus on understanding the concepts behind the laws and formulas, especially the conditions under which they apply. Practice solving problems using Free Body Diagrams. Good luck with your preparation!