Crossfire off South Shore - BOCA race 2015. Yacht navigation requires a good understanding of velocity, distance and time.
1.1 - Variables and Units
Objectives:
- To understand the difference between a variable and a unit
- To know the importance of units
- To be able to convert from one unit to another where necessary
- To be able to rearrange an equation to find the units of a variable
Physics often appears to a myriad of numbers and letters, often weird looking greek ones. Some are the same, which can get confusing. Firstly, what is a variable? A variable is a quantity that can change. For example, your test scores are variables. The amount of money that you have to spend this weekend is a variable. The strength of the wind, the speed of the boat, the direction that you sail in are all variables. Scientists and engineers tend to use shorthand letters for these variables in order to have to keep writing the words in full all the time. Mathematicians came up with the rules for how to jiggle these variables around in a way that makes sense - algebra.
A variable that is fixed is often known as a parameter. This is not terribly important to know at AP level.
Anything that can be measured has to have a unit of measurement. For example: when I worked in Turkey an ice cream cost 3,000,000. Luckily for me it was 3,000,000 Lira, which was equivalent to about $1.50 ish. When measuring something to cut in the workshop it is critical to state the unit - \(6\,\text{feet}\) is very different from \(6 \,\text{inches}\). In the kitchen \(425^{\circ}\text{F}\) is not the same as \(425 ^{\circ}\text{C}\).
So, marks will be regularly deducted for missing units after the answer to a problem! BE WARNED.
AND ANOTHER THING: scientists always use the metric system of measurements. It is just US that still uses the frankly baffling Imperial system. Amusingly, they often refer to it as "standard"! Even though the AP exam is American, it is always in metric.
A variable that is fixed is often known as a parameter. This is not terribly important to know at AP level.
Anything that can be measured has to have a unit of measurement. For example: when I worked in Turkey an ice cream cost 3,000,000. Luckily for me it was 3,000,000 Lira, which was equivalent to about $1.50 ish. When measuring something to cut in the workshop it is critical to state the unit - \(6\,\text{feet}\) is very different from \(6 \,\text{inches}\). In the kitchen \(425^{\circ}\text{F}\) is not the same as \(425 ^{\circ}\text{C}\).
So, marks will be regularly deducted for missing units after the answer to a problem! BE WARNED.
AND ANOTHER THING: scientists always use the metric system of measurements. It is just US that still uses the frankly baffling Imperial system. Amusingly, they often refer to it as "standard"! Even though the AP exam is American, it is always in metric.
A note regarding formatting. When typing variables and units it is easy to get them muddled as the same letters are often used in different contexts. The standard is that variables are written in italics and the unit in normal case with a space after the value. E.g. the symbol for mass is either \(M\) or \(m\), while the symbol for a metre is also \(\text{m}\) and the prefix for mega is \(\text{M}\)! In practice this is not as confusing as it appears. When you write these by hand, the context is determined solely by the location of the symbols.
Try to follow the teacher's formatting and don't randomly change between lower and upper cases.
For example: \(m=13.5\,\text{kg}\) and \(l=3.2\,\text{m}\)
Physics seems to use a lot of equations, although even at AP there are not that many. These follow the basic rules of algebra that you have studied in maths class. It is expected that you are totally fluent in algebra. After all: algebra was sort of invented to solve physics problems...
Top tip - if there is a square root in the equation, get rid of it by squaring everything before trying to rearrange it.
Try to follow the teacher's formatting and don't randomly change between lower and upper cases.
For example: \(m=13.5\,\text{kg}\) and \(l=3.2\,\text{m}\)
Physics seems to use a lot of equations, although even at AP there are not that many. These follow the basic rules of algebra that you have studied in maths class. It is expected that you are totally fluent in algebra. After all: algebra was sort of invented to solve physics problems...
Top tip - if there is a square root in the equation, get rid of it by squaring everything before trying to rearrange it.
ACTIVITY - Discuss the above cartoon!
Trivia Question: Which very commonly used variable has never successfully been given a metric unit?
| cw_0.1_problem_solving_challenges.pdf |
Other Resources
Wonders of Physics - Kinematics. Excellent cartoons from Evan Toh