143k views
0 votes
Show the equation of simple pendulum to be dimensionally consistent

User Yuyu
by
8.2k points

1 Answer

4 votes
T is in seconds (s)

2pi is dimensionless

L is in meters (m)

g is in meters per second squared (m/s^2)

so you can write the equation for the period of the simple pendulum in its units...

s=sqrt(m/(m/s^2))

simplify

s=sqrt(m*s^2*1/m) cancelling the m's

s=sqrt(s^2)

s=s

therefore the dimensions on the left side of the equation are equal to the dimensions on the right side of the equation.
User Simple Simon
by
7.8k points