Physics: Fundamental Quantities and Units

• Physics is a natural science that involves studying matter and its motion through space and time, including energy and force.
• Physics is a fundamental scientific discipline aimed at understanding the behavior of the universe.

Fundamental Quantities and Units

• Physics uses fundamental quantities such as length, mass, and time to describe the universe.
• The SI system uses meter (m) for length, kilogram (kg) for mass, and second (s) for time.
• Derived quantities are expressed using these base units.

Length

• Length measures the distance between two points.
• The meter is the SI unit of length, defined using the speed of light.

Mass

• Mass measures an object's resistance to acceleration.
• The kilogram is the SI unit of mass, defined by the international prototype of the kilogram.

Time

• Time measures the duration of events.
• The second is the SI unit of time, defined by the frequency of radiation emitted by cesium atoms.

Dimensional Analysis

• Dimensional analysis checks relationships between physical quantities by identifying their dimensions.
• The dimension of a physical quantity indicates its relationship to the base quantities.
• Dimensions are expressed using square brackets, such as [L] for length, [M] for mass, and [T] for time.
• Dimensional analysis can verify the consistency of equations.
• If dimensions differ on both sides of an equation, the equation is incorrect.
• Dimensional analysis can derive relationships between physical quantities.

Conversion of Units

• Conversion of units changes a quantity from one unit to its equivalent in another unit.
• Conversion factors are used to convert between different units.
• For example, 1 inch equals 2.54 centimeters, so the conversion factor is 2.54 cm/inch.
• When converting units, multiply the original quantity by the conversion factor, ensuring that the units cancel out correctly.

Significant Figures

• Significant figures are the digits known with certainty in a number, plus one uncertain digit.
• Non-zero digits are always significant.
• Zeros between non-zero digits are significant.
• Leading zeros are not significant.
• Trailing zeros to the right of the decimal point are significant.
• Trailing zeros in a whole number without a decimal point may or may not be significant.
• In calculations, round the result to the same number of significant figures as the least precise measurement.

Accuracy and Precision

• Accuracy indicates how close a measurement is to the true value.
• Precision reflects the repeatability of a measurement.
• A measurement can be precise but not accurate, or accurate but not precise.

Vectors and Scalars

• Scalars are quantities described fully by a magnitude or numerical value.
• Vectors are quantities described fully by both magnitude and direction.

Coordinate Systems

• Coordinate systems describe a point's position in space.
• The Cartesian coordinate system uses three perpendicular axes (x, y, z) to specify a point's position.
• The polar coordinate system uses a radial distance (r) and an angle (θ) to specify a point's position in a plane.
• The cylindrical coordinate system extends the polar coordinate system to three dimensions, using a radial distance (r), an angle (θ), and a height (z).
• The spherical coordinate system uses a radial distance (r), an azimuthal angle (θ), and a polar angle (φ) to specify a point's position in space.

Trigonometry

• Trigonometry studies relationships between sides and angles of triangles.
• Sine, cosine, and tangent are basic trigonometric functions.
• sin(θ) = opposite / hypotenuse
• cos(θ) = adjacent / hypotenuse
• tan(θ) = opposite / adjacent
• The Pythagorean theorem states that in a right triangle, a^2 + b^2 = c^2, where c is the hypotenuse.

Problem-Solving Strategy

• Read the problem and identify what is being asked.
• Draw a diagram to visualize the problem.
• List known and unknown quantities.
• Choose relevant equations.
• Solve the equations for the unknown quantities.
• Check if the answer is reasonable.
• Include units with the answer.