# Units

## 7 Fundamental units

Measurement | Unit | Symbol |

Time | Second | s |

Displacement | Metre | m |

Mass | Kilogram | Kg |

Current | Ampere | A |

Temperature | Kelvin | K |

Amount of substance | Mole | mol |

Luminous Intensity | Candela | cd |

## Derived quantities

To convert between the derived and fundamental units, look at the **formula and substitute the units**.

E.g Momentum has derived unit - p.

To find fundamental, substitute units into the formula.

**p = mass*velocity = kgms ^{-1}**

## Dimensional consistency

This is checking if the units are correct for measurement by converting it to fundamental units and seeing if it fits the equation.

E.g are the units for velocity at^{2}?

ms^{-1 }≠ ms^{-2}s^{2} Therefore this is not dimensionally consistent.

## Metric multipliers and si prefixes

Factor | Name | Symbol | Factor | Name | Symbol |

10^{1} |
deca | d | 10^{-1} |
deci | d |

10^{2} |
hecto | h | 10^{-2} |
centi | c |

10^{3} |
kilo | k | 10^{-3} |
milli | m |

10^{6} |
mega | M | 10^{-6} |
micro | μ |

10^{9} |
giga | G | 10^{-9} |
nano | n |

10^{12} |
tera | T | 10^{-12} |
pico | p |

10^{15} |
peta | P | 10^{-15} |
femto | f |

## Order of magnitude

The **nearest** power of 10.

6.5 x 10^{5} has a magnitude of 10^{6} because 6.5 rounds up to 10.

## Significant figures

**Your answer must** be to **least precise significant figures** in the question you were asked.

# Uncertainties

## What is uncertainty

This is how much a value measured may vary from the actual value.

**Absolute uncertainty:** the same units as the measurements

**percentage uncertainty:** Given as a percentage as measurement

## Precise Vs Accurate

# Uncertainties Practical

IB Physics: Optional Practical: Density of plasticine

# Types of error

Type | Description | Effect on the graph |

Random | Changes every trial | The best fit line will not pass through all the error bars. |

Systematic | Caused by equipment, which is constant for every trial. | Shifts graph vertically or/and horizontally. Error bars represent this error. |

## Rules to determine the uncertainty

**Rounding:** 1 sig fig on exam *OR* don't round for lab report

**Averages: **Range / 2

**Analog Measurements: **For reliable equipment use **plus or minus half smallest division (rounded to 1sf) **or the uncertainty listed on the equipment.

# Combining Uncertainties

## Added or subtracted

**Add** the absolute uncertainty

$\Delta U+\Delta U$

## Multiplied or divided

**Add** the percentage uncertainty

$\Delta U\%+\Delta U\%$

## Raised to a power

**Times** the percentage uncertainty by the **power** (X) of the equation

$X\times \Delta U\%$

## Determine the uncertainty of a series

**Calculate** the range of values using the min and max value** (not the uncertainty).**

$\frac{{V}_{Max}-{V}_{Min}}{2}=\Delta U$

## Determine the uncertainty of x number of oscillations

**Divide** the absolute uncertainty by the number of oscillations.

$\frac{\Delta U}{X}=\Delta U$

## Trigonometric Uncertainty

**Calculate** the range of values using the min and max value** (normal plus and minus the uncertainty).**

$\frac{Cos(V+U)-Cos(V-U)}{2}=\Delta U$

## Exam Tip

**Do not expend a great lot of effort in expressing uncertainties during an examination**, unless specifically instructed. Assess the evidence, use common sense, and (generally) **round-off absolute uncertainty to one significant figure.** An uncertainty of **±0.389s can be rounded to ±0.4s** to agree with the least significant digit position in the measured value.

# Uncertainty graphs

**Gradient uncertainty: **(Maximum gradient - the minimum gradient)/2

**Y-intercept:** Maximum/minimum y-intercept - best fit y-intercept *(largest difference determines maximum or minimum)*

**Error bars: **Shows the uncertainty of the best line based on the systematic error.

# Vectors

## What are Vectors and Scalars?

A vector is a way of representing a quantity with both **magnitude and direction**. It can be represented in two ways. Either the magnitude is stated directly, then it's direction is given as an angle from something. This is useful when working with a polar coordinate system.

**Vector: **Magnitude and direction

**Scalar: **ONLY magnitude

## Examples of vectors and scalars

Vectors |
Scalars |

velocity |
Mass |

displacement |
Time |

Weight |
Distance |

Acceleration |
Length |

## Difficult to remember Vector and scalars quantities

**Electric field strength - Vector****Current - Scalar****Work - Scalar**

## Ways of representing a vector

- A
**plus or minus**next to the magnitude - F = +5N
- An
**arrow**next to the magnitude - F = 5N ⟶
- A
**direction**next to the magnitude - F = 5N right
- An
**angle**next to the magnitude (angles always**starting from positive**x-axis like a unit circle) - F = 5N 0°

## Horizontal and Vertical Components

Split each component into its horizontal and vertical components using trigonometry. Then for each axis add the components together.

## Vector addition and subtraction graphically:

To add two vectors, draw the first vector with its **tail at the origin and then draw the second vector with its tail at the previous vectors head.** Finally, draw a line from the origin to the head of the second vector. This line is the new vector, as shown below.

W= U+V

To subtract a vector, do the same as with addition but flip the vector which you are subtracting.

# Practise Test

Here is a practise test I put together. It is 1hr long and made from V3 Past exam questions.

https://drive.google.com/file/d/1SxW4rSdmN5T4j08TqpJ9cBx3Py5JNOnI/view?usp=sharing

# Editors

- joeClinton - 357 words.
- CD_FER - 570 words.

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