AP

Laws of Motion Notes

Chapter 4: Newton's Laws of Motion

Forces

  • Definition of Force: A force may be defined as any interaction that changes the state of rest or motion of an object.

  • Effects of Forces:

    • i) Can change the speed or direction of an object.

    • ii) Can change the shape of an object.

    • iii) Can change the size of an object.

Aristotle's Fallacy

  • Claim: Aristotle stated that an external force is always required to maintain an object in motion.

  • Corrected View: This is incorrect; internal properties (inertia) are required to maintain an object's state.

Galileo's Experiment

  • Conducted experiments that formulated the Law of Inertia.

  • Inertia Defined: A body at rest will remain at rest and a body in motion will continue moving at a constant speed in a straight line unless acted upon by an external force.

Newton's First Law of Motion

  • Statement: Every body continues in its state of rest or uniform motion in a straight line unless compelled to change that state by an external force.

  • Inertia:

    • Defined as the resistance of an object to any change in its state of motion.

Illustrations of Newton's First Law

  • Inertia of Rest:

    • Case 1: Dust is removed from a hanging carpet by beating it.

    • Case 2: Shaking a tree branch causes its fruits and dry leaves to fall.

    • Case 3: A person feels a backward jerk when a bus starts moving.

  • Inertia of Motion:

    • Case 1: Passengers feel a jerk forward when a moving bus suddenly stops.

    • Case 2: A person feels a forward fall when getting out of a moving bus.

    • Case 3: An athlete takes a sudden leap during a long jump.

Newton's Second Law of Motion

  • Statement: The rate of change of momentum of a body is directly proportional to the applied force and occurs in the direction of that force.

  • Formula: F = ma, where F is force, m is mass, and a is acceleration.

Rate of Change of Momentum

  • Equation:

    • Δp = F dt, where p is momentum and t is time.

Applications of Second Law

  • Impulse and Impulsive Force:

    • An impulsive force is a large force applied over a short period, resulting in a significant change in momentum.

    • Examples:

      • When a batsman hits a ball.

      • When a hammer strikes a nail.

    • Impulse Formula: J = F × t, where J is impulse.

Newton's Third Law of Motion

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

  • Applications:

    • When a book lies on a table, the weight of the book applies a force downwards (gravity), and the table exerts an equal and opposite force upwards (normal force).

Apparent Weight of a Body in a Lift

  • Case 1: When the lift moves upward: Weight (R) increases.

  • Case 2: When the lift moves downward: Weight decreases.

  • Case 3: When the lift moves with constant velocity: Weight remains unchanged.

  • Case 4: If the rope breaks (free fall): Apparent weight becomes zero.

Conservation of Linear Momentum

  • Law: When no external force is acting on a system, the total momentum remains constant.

  • Equation: p_initial = p_final, where p is momentum.

Applications of Momentum Conservation

  • Impulse-momentum theorem states that impulse is equal to the change in momentum.

    • Example: Recoil of a gun after firing a bullet.

Equilibrium of Concurrent Forces

  • Definition: When forces acting at a point balance each other.

  • Condition for Equilibrium: Sum of all forces is zero (∑F = 0).

Friction

  • Definition: The force that opposes relative motion between two surfaces in contact.

  • Types of Friction:

    • Static Friction: Friction between two bodies at rest.

    • Kinetic Friction: Friction when a body moves.

  • Factors Affecting Friction:

    • Nature of surfaces

    • Normal force

Rolling Friction

  • Definition: The force of friction when a body rolls over a surface.

  • Characteristics: Less than sliding friction due to lack of rubbing between surfaces.

Methods to Reduce Friction

  1. Polishing surfaces.

  2. Using lubricants between surfaces.

Banking of Curved Roads

  • Concept: Raising the outer edge of a road to help vehicles maintain speed in a curve while reducing the risk of skidding.

Centripetal Force

  • Definition: The force required for an object to move in a circular path.

  • Formula: F = (mv^2)/r, where F is centripetal force, m is mass, v is speed, and r is radius of the path.

Motion in a Vertical Circle

  • Analyzing tension in a string and forces acting on an object moving in a vertical loop.

  • Key Equations:

    • Tension at various points in the circle and the minimum velocity required at the top point.