## Physical Quantities

A physical quantity is anything that can be measured. Physical quantities can be divided into base quantities and derived quantities. **Base quantities** are those quantities which are distinct in nature and cannot be defined by other quantities. **Derived quantities** are those whose definitions are based on other physical quantities (base quantities).

QUANTITY | SYMBOL | S.I. UNIT NAME | S.I. UNIT SYMBOL |
---|---|---|---|

mass | m | kilogram | kg |

time | t | second | s |

length | l | meter | m |

temperature | T | kelvin | K |

amount of substance | n | mole | mol |

QUANTITY | SYMBOL | DERIVATION | DERIVED UNIT |
---|---|---|---|

area | A | length x length | m^{2} |

volume | V | length x length x length | m^{3} |

density | ρ (pronounced rho) | mass/volume | kg/m^{3} |

velocity | v | length/time | m/s |

concentration | C | amount/volume | mol/dm^{3} |

**However some derived quantities have special units which do not show how they were derived.**

QUANTITY | SYMBOL | DERIVATION | DERIVED UNIT | SPECIAL UNIT |
---|---|---|---|---|

pressure | P | force/area | N/m^{2} | pascal (Pa) |

force | F | mass x acceleration | kgm/s^{2} | newton (N) |

work done | W | force x distance | Nm | joule (J) |

power | P | work/time | J/s | watt (W) |

electric charge | Q | current x time | As | coloumb (C) |

**Fractional units such as m/s, kg/m ^{2} e.t.c can also be expressed using negative indices as ms^{-1}, kgm^{-2} since 1/x = x^{-1}.**

## Measurement instruments

#### Vernier callipers

A vernier calliper is used to measure the distance between two opposite sides of an object. The tips of the calliper are adjusted to fit across the points to be measured and then the caliper is then removed and the distance read by measuring between the tips.

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- Outside jaws : used to measure external length
- Inside jaws : used to measure internal length
- Depth probe : used to measure depth
- Main scale (cm)
- Main scale (inch)
- Vernier (cm)
- Vernier (inch)
- Retainer : used to block/release movable part

A digital caliper measuring a 2 Euros coin

#### Reading a vernier scale

The Main scale reading is 10.0 cm (Immediate left of vernier zero). The main scale and the vernier scale align at the second division of the vernier scale. That represents a vernier scale reading of 0.02 cm since 1 vernier division is equal to 0.01 cm. Therefore the measurement reading is 10 cm + 0.02 cm = 10.02 cm.

#### Micrometer screw gauge

A micrometer screw gauge is a device incorporating a calibrated screw used for accurate measurement of small lengths.

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#### Voltmeter

A voltmeter is an instrument used for measuring electrical potential difference between two points in an electric circuit. Analog voltmeters move a pointer across a scale in proportion to the voltage of the circuit.

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#### Ammeter

An ammeter is a measuring instrument used to measure the current in a circuit. Smaller currents in the milliampere or microampere range, are measured using milliammeters or microammeters.

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#### Measuring cylinder

A measuring cylinder is a laboratory equipment used to measure the volume of a liquid. .

## Density

Density is a measurement of the mass per unit volume of a substance. An object with a greater mass in a certain volume has high density. An object with less mass in the same amount of volume has a low density. Density is found by dividing the mass of an object by its volume.

` ρ = m/V `

where ρ is the density, m is the mass, and V is the volume.

The units of density are kg/m^{3} if the mass is in kg and the volume in m^{3} or g/cm^{3} if the mass is in g and the volume in cm^{3}.

## QUESTION

- If the density of wood is 0.5 g/cm
^{3}what is the mass of - 1 cm
^{3}, - 2 cm
^{3}, - 10 cm
^{3}? - What is the density of a substance of
- mass 100 g and volume 10 cm
^{3}, - volume 3 m
^{3}and mass 9 kg? - The density of gold is 19 g/cm3.
- 38 g,
- 95 g of gold.

- Find the volume of