Observations and Results
When you tucked your weights, you should have spun faster. But the total momentum of all the moving parts remained constant. Confused yet? In order to understand how this makes sense, we need to quickly review momentum and look at what we changed during the spin.
When you began your spin, you caused the whole system—your chair, your body and your weights—to achieve a specific momentum. Let's start by looking at the weights. Like all moving stuff in the universe with mass, the weights have momentum, which makes them want to continue moving in a straight line. They'd do just that if it wasn't for the tension exerted by your arms, which pulls them in a circular path. We can therefore think of the weights as wanting to continue traveling in that same circular path at a constant speed. Hypothetically, they'd be able to travel like this indefinitely if it weren't for air resistance and the friction created by the chair's pivoting column.
Next, you pulled your weights in toward your torso. Would it make any sense for the weights to slow down to match the rotational speed of your body? Nope! Remember—the relatively heavy weights were given momentum at the beginning of your spin when you set them hurtling around the office chair in that large, circular path. By pulling your arms in toward your torso, you moved the weights to a location where they were forced to travel with the same momentum along a much shorter circular path. Unimpeded, they'd complete a full rotation around the chair much faster here. (In fact, because rotational inertia of a weight is proportional to the square of the length of your arm, decreasing your arm's effective length by half should increase the rotational speed of a weight by four times!) But here's the catch—because the weights are in fact attached to your torso by your arms, they actually end up "pulling" your torso along with them, causing you to spin faster in the chair .
Your body doesn't speed up to entirely match the weights’ new speed either, of course—your body's inertia is going to resist this to an extent—but the point is that the momentum of those weights has to go somewhere. Your body gains some momentum, whereas the dumbbells lose some—but the overall momentum of the whole system (atop the chair) stays the same. This is why we often refer to this phenomenon as the conservation of angular momentum. It works in reverse, too—when you reextend your arms, you slow down. This is what enables ice skaters to come out of a spin smoothly!
More to explore
More great science experiments and demonstrations, from Education.com
Angular Momentum and Action–Reaction, from Education.com
Figure Skating Spins, from The Physics of Everyday Stuff
Conservation of Angular Momentum, from YouTube
This activity brought to you in partnership with Education.com