Video Transcript
What are the dimensions of a
quantity that can be measured in units of kilograms times meters squared?
In this question, we’re given a set
of units, and we want to convert them in a sense into dimensions. We see then that dimensions and
units are not the same. A unit, such as a kilogram or a
meter, is a particular way of expressing a physical quantity. A dimension, on the other hand, is
that quantity itself, such as length or time or current. In this compound unit, we see two
individual units. The kilogram is the SI base unit
for mass, and the meter is the SI base unit for length.
Mass and length are physical
quantities that can be measured in units of kilograms and meters. Mass and length then are
dimensions. We represent the dimension of mass
using a capital M and the dimension of length using a capital L. Therefore, if we convert the units
of kilograms meters squared into dimensions, we would get mass times length
squared. We can also write this a bit more
compactly, and we have then our answer. A quantity that is measured in
units of kilograms meters squared has dimensions of mass times length squared.
