Lesson $1$ Units, Trigonometry, and Vectors

Dimensional Analysis

$1.$ In a desperate attempt to come up with an equation to use during an examination, a student

tries v$2=$ ax$.$ Use dimensional analysis to determine whether this equation might be valid.

$2.$ The period of a simple pendulum, defined as the time for one complete oscillation, is

measured in time units and is given by

T $$

$2$

g

$3.$ Newton$$s law of universal gravitation is represented by

Mm

F$$

G

$2$

r

Here F is the gravitational force, M and m are masses, and r is a length. Force has the SI units

kg$$m$/$s$2.$ What are the SI units of the proportionality constant G$?$