Comprehensive Physics and Math Review: Operations, Trigonometry, Units, and Laws

Order of Operations

A set of rules that determines the correct sequence to evaluate a mathematical expression, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).

Evaluate 150 ÷ (6 + 3 x 8) - 5

First, calculate inside the parentheses: 3 x 8 = 24, then 6 + 24 = 30. Next, divide: 150 ÷ 30 = 5. Finally, subtract: 5 - 5 = 0.

Understanding Exponents

Exponents, also known as powers or indices, represent the number of times a base is multiplied by itself.

Directly Proportional

Two quantities are directly proportional if an increase in one results in a proportional increase in the other, as described by Coulomb's law.

Inversely Proportional

Two quantities are inversely proportional if an increase in one results in a proportional decrease in the other, as described by Coulomb's law.

Cross Multiply

A method used to solve proportions, where the product of the means equals the product of the extremes, represented as ad = bc.

Linear Equation

An equation that makes a straight line when graphed, typically in the form y = mx + b, where m is the slope and b is the y-intercept.

Sine Function

A trigonometric function that relates the angle of a right triangle to the ratio of the length of the opposite side to the hypotenuse.

Usefulness of Trigonometry

Trigonometry is useful in real-world applications such as engineering, physics, architecture, and astronomy for calculating angles and distances.

Convert 5/8 to Decimal

5 divided by 8 equals 0.625.

Convert 0.75 to Fraction

0.75 can be expressed as 3/4.

Convert 8.5% to Decimal

8.5% equals 0.085 when converted to decimal.

Convert 0.35 to Percent

0.35 can be expressed as 35%.

Convert 20 m/s to km/h

To convert meters per second to kilometers per hour, multiply by 3.6. Thus, 20 m/s equals 72 km/h.

Examples of Metric Prefix

Examples include kilo- (10^3), centi- (10^-2), and milli- (10^-3).

Newton's Law of Universal Gravitation

This law states that every point mass attracts every other point mass in the universe with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.

Quantum Physics

A branch of physics that studies the behavior of matter and energy at the smallest scales, such as atoms and subatomic particles.

Properties of Plasma

Plasma is a state of matter characterized by ionized gas, high energy, and the ability to conduct electricity and generate magnetic fields.

Kinetic Energy

The energy possessed by an object due to its motion, calculated as KE = 1/2 mv^2, where m is mass and v is velocity.

Potential Energy

The energy stored in an object due to its position or configuration, commonly gravitational potential energy calculated as PE = mgh, where m is mass, g is the acceleration due to gravity, and h is height.

Pressure in Solids vs. Liquids

Pressure in solids is transmitted uniformly in all directions, while in liquids, pressure increases with depth and is transmitted in all directions but is influenced by the weight of the liquid above.

Standing Wave

A wave that remains in a constant position, typically formed by the interference of two waves traveling in opposite directions.

Wave-Particle Duality

The concept in quantum mechanics that every particle or quantum entity exhibits both wave and particle properties.

Pascal's Law

A principle stating that a change in pressure applied to an enclosed fluid is transmitted undiminished throughout the fluid.

Factors Affecting Velocity of Sound

The velocity of sound depends on the medium (solid, liquid, gas), temperature, and pressure.

Convection

The transfer of heat through the movement of fluids (liquids or gases) caused by differences in temperature and density.