Physics - Optics: Unit Conversions

Unit Conversions in Physics

Understanding Units of Measurement

  • Speed Limits:

    • Example: Speed limit is 100 kilometres per hour (km/h)

    • Kilometres (km): Unit for measuring distance

    • Hours (h): Unit for measuring time

    • 100 km/h is considered fast.

  • Alternative Measurement:

    • Example: Speed of 20 metres per second (m/s)

    • Metres (m): Another unit for measuring distance

    • Seconds (s): Another unit for measuring time

    • Conversion Need: To compare 20 m/s to 100 km/h, a unit conversion is required.

Unit Conversion Process

Example 1: Converting Centimetres to Kilometres

  • Conversion Task: Convert 6300 cm to km.

  • Steps to Convert Units:

    • Identify units in conversion helper.

    • Steps from cm to km: 5 steps

    • Direction to move decimal: Left

  • Decimal Movement Process:

    • Move decimal to the left 5 places: 6300 cm → 0.06300 km

    • Final Conversion Result: 6300 cm = 0.063 km

Example 2: Converting Kilograms to Milligrams

  • Conversion Task: Convert 3.1 kg to mg.

  • Steps from kg to mg: 6 steps

  • Direction to move decimal: Right

  • Conversion Result: 3.1 kg = 3,100,000 mg

Practice Exercises:

  1. Convert: 36.4 mm to km

  2. Convert: 2.2055 L to mL

  3. Convert: 42 kg to mg

  4. Convert: 0.4 m to mm

  5. Convert: 8301 mL to kL

  6. Convert: 33 mL to kL

  7. Convert: 8.4 mm to cm

  8. Convert: 3 L to mL

  9. Convert: 36.5 mL to cm³

  10. Convert: 36.4 km to mm

  11. Convert: 0.82 g to mg

  12. Convert: 8.2 L to cm³

  13. Convert: 0.4 mm to m

  14. Convert: 0.82 g to kg

  15. Convert: 505,345 cm³ to kL

  16. Convert: 8.4 cm to mm

  17. Convert: 3400 g to kg

Unit Conversions between km/h and m/s

Challenge: Speed Conversion

  • Problem Statement: Convert 20 m/s into km/h to compare with speed limit of 100 km/h.

Steps for Conversion:

  1. Write the given number and units:

    • $20 ext{ m/s}$

  2. Desired conversion units:

    • To km/h

  3. List the conversion factors:

    • 1000 m = 1 km

    • 60 s = 1 min

    • 60 min = 1 hour

    • 3600 s = 1 hr

  4. Cancelling Units:

    • Convert metres to kilometres first:

      • Place m in the denominator of the second term:

      • This enables cancellation of m.

    • Convert seconds to minutes and then from minutes to hours.

  5. Final Steps:

    • Multiply all numbers on top and divide by all numbers below.

    • Check remaining units to ensure it matches km/h.

Practice Problems for Unit Conversion:

  • (a) Convert 100 km/h into m/s

  • (b) Convert 18 m/s into km/h

  • (c) Speed of light in vacuum: $3.0 imes 10^8 ext{ m/s}$ – Convert to km/h.

    • Speed Conversion Result: $1.08 imes 10^9$ km/h

Final Calculation Example

  1. Multiplying Portions of Conversion:

    • Numerator: Multiply all the numbers on the top and denominator.

  2. Convert to km/h:

    • Result: 72.0 km/h

  3. Simplification Check:

    • Do not leave as fraction; keep one or two decimal points for clarity

Practice:

A car's fuel efficiency is given as 15 km per litre.
Convert this to miles per gallon (mpg), knowing:

  • 1 mile = 1.609 km

  • 1 gallon = 3.785 litres