Order of Magnitude

Since I began teaching “Order of Magnitude” physics a few years ago, I collected many examples of physics estimates from daily life (and the daily life of physicists… which I admit does not necessarily reflect the population as a whole). Here are several examples. More should be added with time!

Solutions using scaling

These are solutions of problems that require scaling (i.e., comparing one the estimated "object" to other similar ones).

• The maximal speed of a row boat.

Solutions using simple dimensional analysis

These solutions require a relatively simple analysis since these problems have only one dimensionless numbers.

• Electric Dipole Radiation.

Elaborate Dimensional Analysis

In more general problems, there are several dimensionless numbers, which makes the analysis more complicated (but not much more!) and often utilizes Buckingham Pi Theorem.

• Gravitational Radiation.

Equipartition

Since different components in a system tend to equilibrate (e.g., the kinetic and potential energies of a system), equipartition is a useful tool in estimates.

• Estimating the oscillation frequency of an LC Circuit.
• Estimating Stellar Parameters using equipartition (including the Chandrasekhar mass limit).

Solutions requiring simple modeling

As a last resort, a problem's approximate solution can often be obtained through simple modeling.

• How long does it take for ice to freeze?
• Estimating the size of dust in a church.
• The rate with which an infectious disease spreads, and the human chain reaction.