1.2. Fundamental Units and Standard Units http://www.ck12.org
FIGURE 1.
A vector requires both a magnitude and
direction.Check Your Understanding
- The density of mercury is 13.5 g/cm^3. What is the formula for density?
Answer: The units of density are given as g/cm^3. Grams are a measure of mass, and cm^3 is a measure of volume.
Density therefore has units of mass/volume. So the formula for density is:d=m/V, wheredis density. Of course,
there may be a “dimensionless” quantity in this formula. Not all formulas have only physical quantities in them.
Consider the volume,V, of a sphere:V=^43 πr^3. Here,ris the radius of the sphere and it has units of length. But the
quantity^43 πhas no units. It is a “pure number.” Dimensional analysis cannot determine what, if any, pure numbers
are in a formula. But, at the very least, a statement of proportionality is always possible, as in the case ofVis
proportional tor^3.
- In the formula,x=^12 at^2 ,xhas units of meters andthas units of seconds. What are the units ofa?
Answer: The acceleration,a, has units of m/s^2.