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[accordion title=”1. 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**.

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[accordion title=”2. 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) |

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[accordion title=”3. Homogeneity of A Physical 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.

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[accordion title=”4. 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** = $$\frac{\Delta x}{x}$$
**Percentage uncertainty** = $$\frac{\Delta x}{x}\times100%$$
- 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 $$\frac{\Delta Y}{Y} = n\frac{\Delta a}{a}$$

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[accordion title=”5. 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.

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[accordion title=”6. 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.

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[accordion title=”7. 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**: $$a^2 = b^2 + c^2-2bc \cos \alpha$$

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