## Base and Derived Quantities

- Physical quantities are classified as base (or fundamental) quantities and derived quantities.

7**base quantities**are chosen to form the base units.

Base Quantity |
Base Unit |

mass | kilogram (kg) |

length | metre (m) |

time | second (s) |

electric current | ampere (A) |

temperature | kelvin (K) |

amount of substance | mole (mol) |

luminous intensity | candela (cd) |

- Any other physical quantities can be derived from these base quantities. These are called
**derived quantities**.

## Prefixes

- Prefixes are attached to a unit when dealing with very large or very small numbers.

Power |
Prefix |

$10^{-12}$ | pico (p) |

$10^{-9}$ | nano (n) |

$10^{-6}$ | micro ($\mu$) |

$10^{-3}$ | milli (m) |

$10^{-2}$ | centi (c) |

$10^{-1}$ | deci (d) |

$10^3$ | kilo (k) |

$10^6$ | mega (M) |

$10^9$ | giga (G) |

$10^{12}$ | tera (T) |

## Homogeneity of Units in an Equation

- A physical equation is said to be homogeneous if each of the terms, separated by plus, minus, equality or inequality signs has the same base units.

## Uncertainty

**Absolute uncertainty**of a measurement of $x$ can be written as $\Delta x$. This means that true value of the measurement is likely to lie in the range $x-\Delta x$ to $x + \Delta x$.**Fractional uncertainty**= $\dfrac{\Delta x}{x}$**Percentage uncertainty**= $\dfrac{\Delta x}{x}\times100%$- If the values of two or more quantities such as $a$ and $b$ are measured and then these are combined to determine another quantity $Y$, the absolute or percentage uncertainty of $Y$ can be calculated as follows:
- If $Y = a\pm b$, then $\Delta Y = \Delta a+\Delta b$
- If $Y = ab$ or $Y = \frac{a}{b}$ , then $\frac{\Delta Y}{Y} =\frac{\Delta a}{a}+\frac{\Delta b}{b}$
- If $Y = a^n$ then $\frac{\Delta Y}{Y} = n\frac{\Delta a}{a}$

## Errors

**Systematic errors**are errors that, upon repeating the measurement under the same conditions, yield readings with error of same magnitude and sign.**Random errors**are errors that, upon repeating the measurement under the same conditions, yield readings with error of different magnitude and sign.

## Accuracy and Precision

- The
**accuracy**of an experiment is a measure of how close a measured value is to the true value. It is a measure of the correctness of the result. - The
**precision**of an experiment is a measure of how exact the result is without reference to what that the result means. It is a measure of how reproducible the results are, i.e. it is a measure of how small the uncertainty is.

## Vectors

- A
**vector**quantity has magnitude and direction. - A
**scalar**quantity has magnitude only. - Addition of vectors in 2D: $\vec{a}+\vec{b}=\vec{c}$
- Subtraction of vectors in 2D: $\vec{a}-\vec{b}=\vec{d}$

- Methods of finding magnitudes of vectors:
- resolution of vectors into perpendicular components
- by scale drawing
- using:

**sine rule**: $\frac{a}{\sin \alpha}=\frac{b}{\sin \beta}=\frac{c}{\sin \gamma}$

**cosine rule**: $a^2 = b^2 + c^2-2bc \cos \alpha$