TERMS

MECHANICS

  • branch of physics that deals with the study of the motion and behavior of physical objects under the influence of forces.

TYPES OF MECHANICS

  • Quantum Mechanics

    • deals with the behavior of particles at the atomic and subatomic scales. It introduces the concept of wave-particle duality, which means that particles like electrons and photons can exhibit both particle-like and wave-like behavior

  • Relativistic Mechanics

    • as Einstein’s theory of relativity, encompasses two theories: Special Relativity and General Relativity. Special Relativity, formulated by Albert Einstein in 1905, deals with the behavior of objects moving at high speeds, close to the speed of light

  • Classical Mechanics

    • as Newtonian mechanics, is the branch of mechanics that deals with the motion of objects at everyday speeds and sizes

LAWS OF MOTION

  1. Inertia

    • A foundational principle in classical mechanics

    • States: "An object at rest will remain at rest and an object in motion will remain in motion in a straight line, unless acted upon by an external net force"

      • Describes the tendency of objects to resist changes in state of motion

    • Objects at rest: Remain at rest unless force applies

    • Objects in motion: Continue moving at constant velocity (speed and direction) unless external force acts to change motion

  2. Force and Acceleration

    • Fundamental principle in classical mechanics

    • Describes the relationship between force, mass, and acceleration

    • States: "The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass"

  3. ACTION-REACTION

    • fundamental principle in classical mechanics

    • Often referred to as the "Law of Action-Reaction"

    • States: "For every action, there is an equal and opposite reaction"

    • Implies that when one object exerts a force on another object, the second object responds with a force of equal magnitude but in the opposite direction

    • Action-reaction pairs of forces always act on different objects

    • Formula: F₁ = -F₂ (Force exerted by object 1 on object 2 is equal in magnitude but opposite in direction to the force exerted by object 2 on object 1)

CONCEPT OF PARTICLES AND RIGID BODY

  • Essential for analyzing the motion and behavior of objects

  • Simplify and model complex systems for analysis

  • Vital in physics for understanding a wide range of physical phenomena

Particle:

  • - Theoretical point mass with no size or shape

  • - Used to represent objects where size and shape can be neglected in analysis

  • - Motion described using Newton's laws of motion and vector operations

  • - Often used to analyze the motion of objects like a baseball, car, or plane

Rigid Body:

  • - Physical object maintaining shape and size under external forces

  • - Motion described using Newton's laws of motion and vector operations

  • - Considers additional concepts like torque and rotational motion

  • - Used to analyze motion of objects like rotating wheels, swinging pendulums, or spinning tops

Vector Operations:

  • Addition of Two Vectors:

    • - Vectors cannot be added by usual algebraic rules.

    • - Triangle Law of Vector Addition is used.

    • The resultant vector is independent of the order of addition (commutative property).

    • - Formula: Vec A + Vec B = Vec C

  • - Triangle Law of Vector Addition:

    • The resultant vector is the third side of the triangle formed by two vectors.

    • - Magnitude of resultant: √(|a|² + |b|² + 2|a||b|cos θ)

  • - Parallelogram Law of Vector Addition:

    • The resultant vector is the diagonal of a parallelogram formed by two vectors.

    • The adjacent side of the parallelogram represents two vectors.

  • - Subtraction of Two Vectors:

    • A negative vector is a vector with an opposite direction.

    • - Subtraction is solved by reversing direction and applying the Triangle Law of Vector Addition.

  • - Multiplication of Vector with Scalar:

    • - The direction of vector remains the same, magnitude changes by a factor of scalar.

    • - Formula: |k Vec A| = k |Vec A|

    • - Magnitude increases when k > 1, decreases when k < 1.

  • - Product of Two Vectors:

    • - Two kinds of multiplication: Scalar Multiplication (Dot Product) and Vector Multiplication (Cross Product).

  • - Dot Product:

    • The result is a scalar quantity.

    • - Formula: Vec a • Vec b = |Vec a||Vec b|cos θ

  • - Cross Product:

    • The result is vector quantity perpendicular to the plane containing the two given vectors.

    • - Formula: Vec a × Vec b = |a||b|sin (θ)n

LESSON 2 Force System:

  • - Coplanar Force System:

    • Lines of action of all forces lie in one plane.

    • Illustrated by forces acting on the same plane.

  • - Non-coplanar Force System:

    • Lines of action of all forces lie in more than one plane.

    • Illustrated by forces acting on different planes.

  • Classification of Force System According to Line of Action:

    • 1. Concurrent Force System:

      • Lines of action pass through a common point.

      • Illustrated by forces passing through point O.

    • 2. Parallel Force System:

      • Lines of action are parallel (along X or Y axis).

      • Illustrated by parallel forces along X or Y axis.

    • 3. Non-Concurrent Force System:

      • Lines of action are neither parallel nor intersect at a common point.

      • Illustrated by forces not meeting at a common point or being parallel.

Scalar and Vector Quantities:

  • Scalars:

    • Possess magnitude only.

    • Added arithmetically.

  • Vectors:

    • Possess direction and magnitude.

    • Combined by geometric addition (vector addition).

Resultant:

  • Minimum system of forces producing the same effect as the original system.

    • May be:

      • Single force.

      • Pair of equal, opposite, and parallel forces (couple).

      • Single force and a couple.

  • Components of a Force:

    • Two or more forces, acting together, produce the same effect as the original force.

EQUILIBRIUM OF FORCE SYSTEM

EQUILIBRIUM

  • deals essentially with the action of forces on bodies that are at rest.

Free-Body Diagram

  • An isolated view of a body which shows only the external forces exerted on the body is called a free-body diagram.