Converting Between Units Physics Lesson 01

Before we get started: Think about when you’re cooking from a recipe. How do you know how much of each ingredient you are going to use?

All recipes give you both a NUMBER and a UNIT. If you use the wrong unit (teaspoons instead of tablespoons), you mess up the recipe. The same is true in physics: If you use the wrong unit, you mess up the calculation.

Why do we use the units we do? The simple answer is: we pick the units that are EASIEST for us to work with. – You would never measure the amount of gasoline that fills your car in teaspoons…that would take forever. Instead, we use gallons. – You would never measure the distance between NY and LA in inches! In order to communicate scientifically with people all over the world, we use SI Units

SI Units This stands for “Système International d'Unités” or in English, the International System. All scientists around the world communicate using these units: – DISTANCE is measured in METERS. (m) – MASS is measured in KILOGRAMS. (kg) – TIME is measured in SECONDS. (s) – There are even more SI units, but we will get to them in later chapters.

What do we do if the units we are given are DIFFERENT than the ones we are WANT? We convert! There are 5 easy steps to converting. 1.IDENTIFY the units we are GIVEN. 2.IDENTIFY the units we WANT. 3.PICK the CONVERSION FACTORS to go from one unit to the other. 4.DRAW a T-CHART and PLUG IN the conversion factors. 5.CANCEL OUT units that show up on both the BOTTOM and TOP. Then just do the math.

EXAMPLE: Erick lives 2.4 miles away from school, and Mr. Brown challenged him to figure out how many feet that was. Help him solve the problem. Step 1: IDENTIFY the units we are GIVEN. “Erick lives 2.4 miles away from school.” Step 2: IDENTIFY the units we WANT. “figure out how many feet that was”

EXAMPLE: Erick lives 2.4 miles away from school, and Mr. Brown challenged him to figure out how many feet that was. Help him solve the problem. Step 3: PICK the CONVERSION FACTORS to go from one unit to the other. Ask yourself, “How are miles related to feet?” You can find this information in charts, in textbooks, and on the internet. 1 mile = 5280 feet

EXAMPLE: Erick lives 2.4 miles away from school, and Mr. Brown challenged him to figure out how many feet that was. Help him solve the problem. Step 4: DRAW a T-CHART and PLUG IN the conversion factors. We always start by putting the units we are GIVEN here. We then always write the units we WANT to get here. We will leave this box empty for now. In later examples we will use it.

EXAMPLE: Erick lives 2.4 miles away from school, and Mr. Brown challenged him to figure out how many feet that was. Help him solve the problem. Step 4: DRAW a T-CHART and PLUG IN the conversion factors. 2.4 MILES5280 FEET 1 MILE

EXAMPLE: Erick lives 2.4 miles away from school, and Mr. Brown challenged him to figure out how many feet that was. Help him solve the problem. Step 5: CANCEL OUT units that show up on both the BOTTOM and TOP. Then just do the math. 2.4 MILES5280 FEET 1 MILE = FEET

Doing the Math The math in physics is exactly the same as the math you’ve done in your math classes. Look at the T-CHART like 2 fractions right next to each other. – If there are two numbers on the TOP, MULTIPLY them. – If there are two numbers on the BOTTOM, MULTIPLY them. – If there is one number on TOP and one on BOTTOM, DIVIDE them.

Multi-Step Conversions Not all conversions will be simple enough to do in just one step. The 5 rules for converting are still the same, you will just need to use more conversion factors. For example, what if Mr. Brown had asked Erick to convert his distance from miles to inches? What would Erick do?

Solving Multi-Step Conversions There are two ways to solve multi-step conversions: 1.You can solve one conversion, get the answer, and then plug it into the next conversion as your given. 2.You could draw one long T-Chart and use many conversion factors at once. **Both of them are equally correct. CHOOSE the one that YOU feel COMFORTABLE with!

EXAMPLE: Let’s figure out how many inches away from school Erick’s house is. Steps 1-3 are the same, no matter which way you solve it. – Step 1: Erick lives 2.4 miles from school. – Step 2: How many inches away does Erick live? – Step 3: 1 mile = 5280 feet 1 foot = 12 inches

EXAMPLE: Method 1: Solve, plug, solve 2.4 MILES5280 FEET 1 MILE = FEET 12 INCHES 1 FOOT = INCHES FEET

EXAMPLE: Method 2: One big conversion 2.4 MILES5280 FEET 1 MILE 12 INCHES 1 FOOT = INCHES