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Dimensional Analysis

Dimensional analysis is a crucial tool used to convert units of measurement, requiring an understanding of ratios that equal 1. For example, various ratios like 60 seconds = 1 minute, and 5280 feet = 1 mile help in the conversion process. You can simplify calculations by cross-reducing units as you would with fractions, ensuring the final answer reflects the desired units. For instance, converting a car's speed from 65 miles per hour to feet per second involves utilizing these techniques. Practice problems help solidify your understanding of these conversions.

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Dimensional Analysis

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  1. Dimensional Analysis

  2. Measurement Ratios • In order to use dimensional analysis, you have to understand that you need to use ratios that have a value of 1 to change the units of measurement. • Example 60 sec5280 ft 12 in 1 min 1 mile 1 ft These are all examples of ratios that equal 1 because the measurement in the numerator is equal to the measurement in the denominator.

  3. Cross Reducing • Just as you cross reduce fractions whenever possible, you want to cross reduce the units of measurement until you get the units you want in your answer. Example: ½ x ⅔ You cross reduce the 2s to get the answer ⅓ 25 mi x 2 hr 1 hr 120 min The hr unit of measurement cancels out so that all that is left is miles/minutes.

  4. Example Problem • A car is traveling 65 miles/hr. How many feet per second is it traveling? 65 miles x 5280 ft. x 1 hour x 1 minute = feet 1 hour 1 mile 60 min 60 sec sec Cancel out all units of measurement that can be cross reduced. When all that is left is feet/sec, which is what you want, then you just work with the numbers. 65 x 5280 x 1 x 1 1 1 60 60 Now cross reduce as much as you can, multiply across, then divide. The result will be the number of feet per second you are traveling when going 65 mph. Answer: 95.3 feet/sec

  5. Practice Problems • How many seconds are there in one week? • How many ounces are in one ton? • How many cups in one gallon?

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