CHANGING UNITS

Ian Cooper

email matlabvisualphysics@gmail.com

A skill that you must master is to change one unit in to another. For example, years into seconds, and km.h^-1 to m.s^-1.

Example 1 Simple time conversions

It is often necessary to convert one set of units into another. This can be done by reducing the conversion to a simple algebraic problem. The following examples will illustrate how to do this.

Example 2

A car is travelling at a speed of 165 km.h^-1. What is the speed of the car in m.s^{-1 ?}

1 km = 10³ m 1 h = (60)(60) s = 3.6´10³ s

1 km. h^-1= (10³) / (3.6´10³) m.s^-1

165 km.h^-1= (165) (10³) / (3.6´10³) m.s^-1 = 45.8 m.s^-1

Example 3

The density of a liquid was 1.8 g.mL^-1. What is the density in kg.m^{-3 ?}

1 g = 10^-3 kg

1 mL = 1 cm³

1 cm = 10^-2 m

1 cm³ = (10^-2)³ cm³= 10^-6 m³

1 g.mL^-1 = (10^-3) / (10^-6) kg.m^-3

1.8 g.mL^-1 = (1.8) (10^-3) / (10^-6) kg.m^-3 = 1.8´10³kg.m^-3

Note

The use of multiplication by powers of 10 (x10⁶).

The use of superscripts:

use m.s^-1 not m/s

use kg.m^-3 not kg/m³