## A-Level H2 Physics Notes

# Chapter 1: Measurements

# Summary:

SI Units:

There are 7 base units:

Meters (m), Kilogram (kg), Second (s), Ampere (A), Kelvin (K), Mole (Mol), and Candela (cd)

Each unit corresponds with one of the 7 physical quantities:

Length, Mass, Time, Current, Temperature, Amount of Substance, and Light Intensity.

Base Quantity | Symbol | SI Units | Base Unit / Symbol for Units |
---|---|---|---|

Length | 𝓛 | metre | m |

Mass | m | kilogram | kg |

Time | t | second | s |

Current | I | ampere | A |

Temperature | T | Kelvin | K |

Luminous Intensity | L | candela | cd |

Amount of Substance | n | mole | mol |

Derived Units:

Any unit that is defined in terms of the base units. They are expressed as products or quotients of base units.

Derived Quantities | Equation | Derived Units |
---|---|---|

Volume (V) | V=L^3 | m^3 |

Area (A) | A=L^2,L ∶ Length | m^2 |

Acceleration (a) | a=Δv/Δt, Δ : "change in" | m s^-2 |

Velocity (v) | v=L/t, t : time | m s^-1 |

Density (ρ) | ρ=m/V, m : mass | kg m^-3 |

Force (N) | F=ma, m : mass, a : acceleration | kg m/s^2 |

Momentum (p) | p=mv | kg m s^-1 |

Work Done | W=fd, f : force, d : distance | (kg m^2)/s^2 |

Voltage | V=w/q, w : work done, c : charge, c=It, I : current; V=w/(It) | (kg m s^-2)/(s^3 *A) |

Homogenous Equations:

An equation is said to be homogenous or dimensionally consistent if every term on both sides of the equation has the same base units.

A homogenous equation may not be true or correct.

Systematic Errors:

When all the readings of an experiment are consistently larger or smaller than the true value by a fixed amount.

Random Errors:

When the readings of an experiment are randomly scattered about a mean value.

Accuracy:

The degree of closeness of the experimental values to the true value.

Measured by comparing the average of multiple experimental readings to the true value.

Precision:

The degree of agreement between repeated measurements of the same quantity.

Scalar Quantity:

Physical quantities with magnitude only.

Vector Quantity:

Physical quantities with both magnitude and direction.

Prefix:

Signifies powers of 10, written before numbers to make them easier to read and understand.

Power | Prefix | Symbol |
---|---|---|

10^12 | Tera | T |

10^9 | Giga | G |

10^6 | Mega | M |

10^3 | Kilo | k |

10^-1 | Deci | d |

10^-2 | Centi | c |

10^-3 | Milli | m |

10^-6 | Micro | µ |

10^-9 | Nano | n |

10^-12 | Pico | p |

Uncertainty:

Uncertainty is the range of possible values within which the true value of the measurement lies.

1. | Addition | R=aX + bY | Absolute Uncertainty is ΔR=|a|ΔX+|b|ΔY |
---|---|---|---|

2. | Subtraction | R = aX - bY | Absolute Uncertainty is ΔR=|a|ΔX+|b|ΔY |

3. | Product | R = aX * bY | Fractional Uncertainty is ΔR/R = ΔX/X + ΔY/Y |

4. | Division | R = aX/Y | Fractional Uncertainty is ΔR/R = ΔX/X + ΔY/Y |

5. | Product with Powers | R = (aX^m) * (Y^n) | Fractional Uncertainty is ΔR/R = |m|(ΔX/X) + |n|(ΔY/Y) |

6. | Quotient with Powers | R = (aX^m)/(Y^n) | Fractional Uncertainty is ΔR/R = |m|(ΔX/X) + |n|(ΔY/Y) |

7. | Special Functions | Any functions such as sine, cosine, etc. | Uncertainty of R is (Rmax + Rmin)/2, R = (Rmax + Rmin)/2 ± (Rmax - Rmin)/2 |