Let the units find the law

Raise length, gravity and mass to powers until the units come out in seconds.

Interactive

your guess has unitsm

period needss

Find

Power of length1Power of gravity0Power of mass0

The math, with your numbers

T \sim L \quad\to\quad \text{m}

\text{needed: } \text{s}

Units can't tell you pure numbers like 2π, but they pin down how the answer depends on each quantity.

Try this

→Pendulum: what power of the mass do you need? What does that tell you about heavy pendulums?
→Wave on a string: does the string's length matter for the wave speed?
→Orbit: you've just found Kepler's third law. How does the period change if the radius is 4 times bigger?

Want to know why it behaves like this?

The lesson “Dimensional Analysis: Let the Units Do the Work” explains it step by step: Can you find a law of physics just by checking its units?

Let the units find the law

Raise length, gravity and mass to powers until the units come out in seconds.

Let the units find the law

Interactive

your guess has unitsm

period needss

Find

Power of length1Power of gravity0Power of mass0

The math, with your numbers

T \sim L \quad\to\quad \text{m}

\text{needed: } \text{s}

Units can't tell you pure numbers like 2π, but they pin down how the answer depends on each quantity.

Try this

→Pendulum: what power of the mass do you need? What does that tell you about heavy pendulums?
→Wave on a string: does the string's length matter for the wave speed?
→Orbit: you've just found Kepler's third law. How does the period change if the radius is 4 times bigger?

Want to know why it behaves like this?

The lesson “Dimensional Analysis: Let the Units Do the Work” explains it step by step: Can you find a law of physics just by checking its units?