class 11 notes

Class 11 Physics Notes Chapter 5 (Laws of motion) – Physics Part-I Book

Philoid

Philoid

— 8 min read

Physics Part-I
Detailed Notes with MCQs of Chapter 5: Laws of Motion from your NCERT Class 11 Physics textbook. This chapter is fundamental not just for your Class 11 understanding but forms the bedrock for many concepts tested in government exams. Pay close attention to the definitions, laws, and applications.

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

1. Introduction & Historical Context

  • Dynamics: The branch of mechanics dealing with the cause of motion (Force). Contrasts with Kinematics (description of motion without cause).
  • Aristotle's Fallacy: Believed an external force is required to keep a body moving with uniform velocity. This is incorrect in the absence of friction/resistance.
  • Galileo's Contribution: Through experiments with inclined planes, Galileo concluded that a body moving uniformly does not need a force to maintain its motion (in the absence of friction). He introduced the concept of Inertia.

2. Inertia

  • Definition: The inherent property of a body by virtue of which it cannot change its state of rest or of uniform motion along a straight line by itself.
  • Measure of Inertia: Mass is the measure of inertia. A heavier body has more inertia (more resistance to change in its state of motion) than a lighter body.
  • Types (Conceptual):
    • Inertia of Rest: Resistance to change from a state of rest (e.g., dust particles flying off a carpet when beaten).
    • Inertia of Motion: Resistance to change from a state of uniform motion (e.g., passenger falling forward when a moving bus stops suddenly).
    • Inertia of Direction: Resistance to change in direction of motion (e.g., sparks flying tangentially from a grinding wheel).

3. 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 to change that state by forces impressed upon it."
  • Key Concepts:
    • Defines Force qualitatively: Force is that external agent which changes or tends to change the state of rest or of uniform motion of a body.
    • Defines Inertia.
    • Provides the concept of an Inertial Frame of Reference: A frame where Newton's first law is valid (non-accelerating frames). Earth is approximately an inertial frame for many practical purposes.

4. Momentum (Linear Momentum)

  • Definition: The quantity of motion possessed by a body. It is measured as the product of the mass (m) of the body and its velocity (v).
  • Formula: p = mv
  • Nature: It is a vector quantity. Its direction is the same as the direction of velocity.
  • SI Unit: kg m s⁻¹
  • Dimensional Formula: [M L T⁻¹]

5. 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 always in the direction of the applied force."
  • Mathematical Form:
    • F ∝ dp/dt
    • F = k (dp/dt)
    • Choosing k=1 in SI units, F = dp/dt
  • Derivation of F = ma:
    • F = d(mv)/dt
    • If mass 'm' is constant, F = m (dv/dt)
    • Since acceleration a = dv/dt, F = ma
  • Key Concepts:
    • Provides a quantitative definition of Force.
    • Force is a vector quantity.
    • SI Unit of Force: Newton (N). 1 N = 1 kg m s⁻² (The force required to accelerate a 1 kg mass by 1 m/s²).
    • CGS Unit of Force: Dyne. 1 Dyne = 1 g cm s⁻².
    • Relation: 1 N = 10⁵ Dyne.
    • Dimensional Formula of Force: [M L T⁻²]

6. Impulse (J)

  • Definition: The effect of a large force acting for a very short duration. It is measured as the product of the force and the time duration for which it acts.
  • Formula: J = F_avg × Δt (where Δt is the short time interval)
  • Impulse-Momentum Theorem: From Newton's Second Law, F = dp/dt => F dt = dp. Integrating over a short time interval Δt:
    ∫ F dt = ∫ dp => J = Δp = p_final - p_initial
    Impulse is equal to the change in linear momentum.
  • Nature: Vector quantity (direction same as force/change in momentum).
  • SI Unit: N s or kg m s⁻¹ (Same as momentum).
  • Applications: Catching a ball (increasing time reduces force), shock absorbers, airbags.

7. Newton's Third Law of Motion

  • Statement: "To every action, there is always an equal and opposite reaction."
  • Explanation: Forces always occur in pairs. If body A exerts a force F_AB on body B (action), then body B exerts an equal and opposite force F_BA on body A (reaction).
    F_AB = - F_BA
  • Key Characteristics of Action-Reaction Pairs:
    • They are equal in magnitude.
    • They are opposite in direction.
    • They act simultaneously.
    • They act on different bodies. (Therefore, they never cancel each other out).
  • Examples: Walking (pushing ground backward, ground pushes forward), swimming, recoil of a gun, rocket propulsion.

8. Conservation of Linear Momentum

  • Principle: If the net external force acting on a system of particles 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. This implies p = constant.
    For a system of particles: p₁ + p₂ + ... + p_n = constant.
    m₁v₁ + m₂v₂ + ... + m_nv_n = constant (if F_ext = 0).
  • Applications:
    • Collisions (elastic and inelastic).
    • Recoil of a gun: m_g v_g + m_b v_b = 0 => v_g = - (m_b / m_g) v_b (Negative sign shows opposite direction).
    • Explosion of a bomb.
    • Rocket propulsion (based on expelling mass backward).

9. Equilibrium of a Particle

  • Definition: A particle is said to be in equilibrium if the net external force acting on it is zero.
  • Condition: ΣF = 0 or F_net = 0.
    In terms of components: ΣF_x = 0, ΣF_y = 0, ΣF_z = 0.
  • Concurrent Forces: Forces whose lines of action intersect at a common point. A particle under the action of concurrent forces is in equilibrium if their vector sum is zero.
  • Lami's Theorem (for equilibrium under 3 concurrent forces): If a particle is in equilibrium under the action of three concurrent forces F₁, F₂, F₃, then:
    F₁ / sin α = F₂ / sin β = F₃ / sin γ
    where α is the angle opposite F₁, β is the angle opposite F₂, and γ is the angle opposite F₃.

10. Common Forces in Mechanics

  • Weight (W): The gravitational force exerted by the Earth on an object. W = mg, where g is acceleration due to gravity. Always acts vertically downwards.
  • Normal Reaction (N or R): The component of the contact force perpendicular to the surface, exerted by the surface on the object. It adjusts itself up to a limit to prevent the object from penetrating the surface. It is NOT always equal to mg.
  • Tension (T): The restoring force in a stretched string or rope. It acts along the string, away from the object it is attached to. Assumed massless and inextensible in ideal problems.
  • Friction: A force that opposes relative motion (or tendency of relative motion) between surfaces in contact.
    • Static Friction (f_s): Opposes the tendency of relative motion. It is self-adjusting. 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.
    • Kinetic Friction (f_k): Opposes the actual relative motion. It is approximately constant for moderate speeds. f_k = μ_k N, where μ_k is the coefficient of kinetic friction.
    • Properties:
      • μ_k < μ_s generally.
      • Friction depends on the nature of surfaces in contact and the normal reaction (N).
      • Friction is largely independent of the area of contact.
    • Rolling Friction: Friction when a body rolls over a surface. It is much smaller than static or kinetic friction (μ_r << μ_k < μ_s).

11. Circular Motion Dynamics

  • Centripetal Force (F_c): The net force required to keep an object moving in a circular path at constant speed. It is always directed towards the center of the circle.
  • Formula: F_c = mv²/r = mω²r (where v is linear speed, ω is angular speed, r is radius).
  • Important: Centripetal force is not a new kind of force. It is the role played by existing forces (like tension, friction, gravity, normal force, or their components) that provides the necessary inward acceleration.
  • Examples:
    • Stone tied to string: Tension provides F_c.
    • Car on level circular road: Static friction provides F_c (v_max = √(μ_s rg)).
    • Banking of Roads: Component of Normal Reaction provides F_c, reducing reliance on friction. Angle of banking: tan θ = v² / rg (for zero friction).

12. Problem Solving Strategy: Free Body Diagrams (FBD)

  • Isolate the object(s) of interest.
  • Draw all the external forces acting on that specific object. Represent forces as arrows originating from the object (or point particle).
  • Choose a suitable coordinate system.
  • Resolve forces into components along the chosen axes.
  • Apply Newton's Second Law (ΣF_x = ma_x, ΣF_y = ma_y) or conditions for equilibrium (ΣF_x = 0, ΣF_y = 0).
  • Solve the resulting equations.

Multiple Choice Questions (MCQs)

  1. A passenger sitting in a bus moving at a constant velocity feels a push backward when the bus suddenly accelerates forward. This is explained by:
    a) Newton's Second Law
    b) Newton's Third Law
    c) Law of Conservation of Momentum
    d) Inertia of Rest

  2. The rate of change of linear momentum of a body is equal to:
    a) Impulse
    b) Net external force
    c) Work done
    d) Kinetic energy

  3. Action and reaction forces mentioned in Newton's third law:
    a) Act on the same body
    b) Act on different bodies
    c) Are always equal to weight
    d) Cancel each other out

  4. A bullet of mass 20 g is fired from a rifle of mass 8 kg with a velocity of 100 m/s. The recoil velocity of the rifle is:
    a) -0.25 m/s
    b) -2.5 m/s
    c) -0.025 m/s
    d) -25 m/s

  5. Impulse is dimensionally equivalent to:
    a) Force
    b) Power
    c) Energy
    d) Linear Momentum

  6. A block is placed on a rough horizontal surface. A force is applied to pull it. The frictional force acting on the block before it starts moving is:
    a) Kinetic friction
    b) Limiting friction
    c) Static friction
    d) Rolling friction

  7. Which of the following statements about friction is incorrect?
    a) Kinetic friction is generally less than limiting static friction.
    b) Frictional force depends on the area of contact.
    c) Coefficient of static friction depends on the nature of surfaces.
    d) Rolling friction is much smaller than sliding friction.

  8. A body of mass 'm' is moving in a circle of radius 'r' with constant speed 'v'. The work done by the centripetal force in one complete revolution is:
    a) (mv²/r) × 2πr
    b) mv²/r
    c) Zero
    d) πr (mv²/r)

  9. 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, thus reducing the force
    d) Decrease the time of impact, thus reducing the force

  10. If the net external force on a system of particles is zero, which quantity must remain constant?
    a) Total kinetic energy
    b) Total potential energy
    c) Total linear momentum
    d) Total angular momentum (assuming no external torque)

Answer Key for MCQs:

  1. d) Inertia of Rest (The body tends to remain at rest relative to its initial frame, hence feels pushed back relative to the accelerating bus).
  2. b) Net external force (Direct statement of Newton's Second Law: F = dp/dt).
  3. b) Act on different bodies (A key characteristic of action-reaction pairs).
  4. a) -0.25 m/s (Conservation of momentum: m_b v_b + m_g v_g = 0 => (0.02 kg)(100 m/s) + (8 kg) v_g = 0 => 2 + 8v_g = 0 => v_g = -2/8 = -0.25 m/s).
  5. d) Linear Momentum (Impulse J = Δp, so units and dimensions are the same).
  6. c) Static friction (It opposes the tendency of motion before movement starts).
  7. b) Frictional force depends on the area of contact. (Friction is largely independent of the apparent area of contact).
  8. c) Zero (Centripetal force is always perpendicular to the displacement vector (velocity) at every point. Work done = F . d cos θ. Here θ = 90°, so cos 90° = 0).
  9. c) Increase the time of impact, thus reducing the force (Impulse J = FΔt = Δp. By increasing Δt, F decreases for the same change in momentum Δp).
  10. c) Total linear momentum (Direct statement of the Law of Conservation of Linear Momentum).

Study these notes thoroughly. Focus on understanding the concepts behind the laws and formulas, and practice applying them using Free Body Diagrams. Good luck with your preparation!

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