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.