Measurement, Proportion, and Vector Concepts (Video Notes)

A set of vocabulary-style flashcards covering measurement accuracy and precision, errors, proportional relationships, vector addition/resolution, and basic trigonometry from the video notes.

Accuracy

The closeness of a measured value to the true or accepted value.

Precision

The degree of exactness or reproducibility of a measurement.

Systematic error

A bias that consistently shifts measurements in the same direction due to instrument or method limitations.

Random error

Unpredictable fluctuations in measurements caused by factors like noise, vibrations, or operator variability.

Calibration

Adjusting an instrument to align its readings with a standard or known value.

Direct proportion

A relationship where one quantity increases in direct ratio to another; y = kx (e.g., circumference proportional to diameter: C = πd).

Inverse proportion

A relationship where one quantity decreases as another increases; y = k/x (e.g., pressure and volume: P·V = constant).

Direct square proportion

A relationship where one quantity is proportional to the square of another (e.g., area A = πr²).

Inverse square proportion

A relationship where one quantity is proportional to the inverse of the square of another (e.g., mv² = k in some contexts).

Constant of variation

The proportionality constant k in equations of the form y = kx.

Circumference

The distance around a circle; for a circle, C is proportional to diameter with C = πd.

Area of a circle

The region inside a circle, given by A = πr².

Vector

A quantity with both magnitude and direction used to describe physical quantities.

Resultant vector

The single vector that represents the combined effect of two or more vectors.

Vector resolution

The process of breaking a vector into perpendicular components.

x-component (horizontal component)

The portion of a vector along the x-axis; for a force F at angle θ, Fₓ = F cos θ.

y-component (vertical component)

The portion of a vector along the y-axis; for a force F at angle θ, Fᵧ = F sin θ.

Pythagorean theorem

In a right triangle, c² = a² + b², used to find a vector’s magnitude from perpendicular components.

Sine

Trigonometric function sin θ = opposite/hypotenuse in a right triangle.

Cosine

Trigonometric function cos θ = adjacent/hypotenuse in a right triangle.

Tangent

Trigonometric function tan θ = opposite/adjacent in a right triangle.

Magnitude

The length or size of a vector; for components, the resultant magnitude is √(Σx)² + (Σy)².

Direction

The angle or orientation of a vector relative to a reference axis, often found using tan⁻¹(Fᵧ/Fₓ).

Significant figures

Digits that contribute to a measurement's precision; typically non-zero digits plus certain zeros.

Rule: non-zero digits are significant

All non-zero digits are significant in a measurement.

Rule: zeros between non-zero digits are significant

Zeros between non-zero digits are significant.

Rule: leading zeros are not significant

Zeros to the left of the first non-zero digit are not significant.

Rule: filler zeros to the right of decimal are not significant

Zeros to the right of a decimal place used as fillers are not considered significant in these notes.