Heavy or light pendulum
Which swings faster, a heavy ball or a light one?
The question
Hang a heavy ball and a light ball on strings of the same length. Which one swings faster?
Have a guess, then show the answer
Neither. They stay in step. A pendulum's swing time depends on its length, not its weight.
Play
Race two pendulums
Change each ball's weight and each string's length, then count the swings. Which change makes a difference?
Different weights, same string: they stay in step.
What's happening
- 1
Gravity pulls harder on the heavy ball, but the heavy ball is also harder to get moving. The two cancel exactly, so both balls speed up the same way.
- 2
What does change the timing is the string. A longer string means a wider arc to travel and a gentler pull along it, so each swing takes longer.
- 3
Make the string a quarter as long and it swings twice as often. Four times as long, half as often.
- 4
That's why old clocks were set by a pendulum's length, and why the 660-tonne damper ball in Taipei 101 is tuned by the length of its cables.
The maths
For small swings, the time for one full swing (there and back) is
L is the string's length and g is gravity (9.81 m/s²). The ball's mass isn't in it at all. A 1 m pendulum takes about 2 seconds a swing; a 25 cm one, about 1 second.
Simplified, and sources
True for small swings (about 10 to 15 degrees); big swings take slightly longer. In air, a light ball's swing shrinks a little sooner than a heavy one's, but its timing stays the same.