Forces and Motion

Forces and Motion

Types of Forces:

• Contact Forces: Forces that act through physical contact between objects, e.g. friction, normal force, and tension.
• Non-Contact Forces: Forces that act without physical contact, e.g. gravitational force, magnetic force, and electrostatic force.

Newton's Laws of Motion:

1. First Law (Inertia): An object at rest will remain at rest, and an object in motion will continue to move with a constant velocity, unless acted upon by an external force.
2. Second Law (F = ma): The force applied to an object is equal to the mass of the object multiplied by its acceleration.
3. Third Law (Action and Reaction): For every action, there is an equal and opposite reaction.

Motion:

• Distance: The total length of the path traveled by an object.
• Displacement: The shortest distance between the initial and final positions of an object.
• Speed: The distance traveled by an object per unit of time.
• Velocity: The rate of change of an object's displacement.
• Acceleration: The rate of change of an object's velocity.

Materials and Their Properties

Physical Properties:

• Density: The mass of an object per unit volume.
• Solubility: The ability of a substance to dissolve in a solvent.
• Conductivity: The ability of a material to conduct heat or electricity.
• Malleability: The ability of a material to be shaped or molded without breaking.
• Ductility: The ability of a material to be stretched or drawn without breaking.

Chemical Properties:

• Reactivity: The ability of a substance to react with other substances.
• Flammability: The ability of a substance to catch fire.
• Toxicity: The degree to which a substance is poisonous or harmful.

Types of Materials:

• Metals: Typically hard, shiny, and good conductors of electricity, e.g. iron, copper, and gold.
• Non-Metals: Typically dull, brittle, and poor conductors of electricity, e.g. carbon, sulfur, and oxygen.
• Ceramics: Inorganic, non-metallic materials, e.g. clay, porcelain, and glass.
• Polymers: Long chains of repeated molecules, e.g. plastics, fibers, and rubbers.

Forces and Motion

Types of Forces:

• Contact Forces occur through physical contact between objects, including friction, normal force, and tension.
• Non-Contact Forces occur without physical contact, including gravitational force, magnetic force, and electrostatic force.

Newton's Laws of Motion:

• First Law (Inertia): An object remains at rest or maintains its velocity unless acted upon by an external force.
• Second Law (F = ma): Force equals mass multiplied by acceleration.
• Third Law (Action and Reaction): Every action is met with an equal and opposite reaction.

Motion:

• Distance: The total length of an object's path traveled.
• Displacement: The shortest distance between an object's initial and final positions.
• Speed: The distance traveled per unit of time.
• Velocity: The rate of change of an object's displacement.
• Acceleration: The rate of change of an object's velocity.

Materials and Their Properties

Physical Properties:

• Density: The mass of an object per unit volume.
• Solubility: The ability of a substance to dissolve in a solvent.
• Conductivity: The ability of a material to conduct heat or electricity.
• Malleability: The ability of a material to be shaped or molded without breaking.
• Ductility: The ability of a material to be stretched or drawn without breaking.

Chemical Properties:

• Reactivity: The ability of a substance to react with other substances.
• Flammability: The ability of a substance to catch fire.
• Toxicity: The degree to which a substance is poisonous or harmful.

Types of Materials:

• Metals: Typically hard, shiny, and good conductors of electricity, e.g. iron, copper, and gold.
• Non-Metals: Typically dull, brittle, and poor conductors of electricity, e.g. carbon, sulfur, and oxygen.
• Ceramics: Inorganic, non-metallic materials, e.g. clay, porcelain, and glass.
• Polymers: Long chains of repeated molecules, e.g. plastics, fibers, and rubbers.

Equations

Definition

• An equation is a statement that expresses the equality of two mathematical expressions, often containing variables.

Types of Equations

• Simple Equations: variable is isolated on one side of the equation, e.g., 2x = 6
• Linear Equations: highest power of the variable(s) is 1, e.g., 2x + 3 = 5
• Quadratic Equations: highest power of the variable(s) is 2, e.g., x^2 + 4x + 4 = 0
• Polynomial Equations: variables are raised to non-negative integer powers, e.g., x^3 - 2x^2 - 5x + 1 = 0

Properties of Equations

• Reflexive Property: a = a
• Symmetric Property: if a = b, then b = a
• Transitive Property: if a = b and b = c, then a = c
• Addition and Subtraction Properties: a = b if and only if a + c = b + c or a - c = b - c
• Multiplication and Division Properties: a = b if and only if ac = bc or a/c = b/c (c ≠ 0)

Solving Equations

• Addition and Subtraction: isolate the variable by adding or subtracting the same value to both sides of the equation
• Multiplication and Division: isolate the variable by multiplying or dividing both sides of the equation by the same non-zero value
• Distributive Property: expand and simplify expressions, e.g., 2(x + 3) = 2x + 6

Special Equations

• Conditional Equations: true only under certain conditions, e.g., x + 1 = 2 (true only if x = 1)
• Identical Equations: true for all values of the variable, e.g., x + x = 2x