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Swiveling Science: Conserving Momentum in a Spinning Chair

Learn how figure skaters speed up during a spin with this dizzying activity
bsh spinning chair


What spins up? Take a spin in a chair to learn about conservation of momentum--and how figure skaters control their spins so well.
George Retseck

Key concepts
Momentum
Inertia
Acceleration

Introduction
Have you ever wondered why figure skaters are able to spin like a top so quickly? In many cases they're able to increase their speed without pushing off of anything simply by tucking their arms in to add any extra force to the spin. What's going on? To find out, we'll mimic the same basic technique figure skaters use and learn about some simple principles from classical mechanics to get to the bottom of how it works. Don't worry—no special coordination or skills are required! All you'll need is a sturdy, swiveling chair and a pair of light dumbbells or heavy books.

Background
Any physical object resists change in its motion, including a change in direction. Isaac Newton described this behavior in his first law of motion: An object's tendency is to either sit still or move in a straight line at a constant speed unless it is acted on by an outside force. This tendency to resist a change in motion is called inertia, and heavier (more massive) objects are more resistant to changes in motion, because the more mass an object has, the more inertia it has.

Think of it this way: What's a harder thing to stop in its tracks—a train traveling at 20 miles per hour, or marble traveling at 20 miles per hour? A marble might be a relatively easy thing to grab, but because of how inertia works, if you tried to grab a moving train, that train would just pull you right along with it. That train is harder to stop because it has a colossally greater momentum than the marble does, even though they are moving at the same speed. That's because momentum is dependent on both velocity and mass (inertia). Keep this in mind as you conduct the following experiment, and also be mindful of the fact that momentum doesn't just disappear—it has to go somewhere!

Materials
● Swiveling chair (An office, desk or any other swiveling chair that spins freely will do.)
● Pair of light dumbbells or heavy books

Preparation
● Set up your swivel chair in the center of a room. (Make sure you'll have enough room to spin with outstretched arms without striking any objects or hurting yourself!)
● This experiment is best performed on a carpeted floor. Try to avoid doing it on a hardwood floor, as our goal is to make sure the caster wheels on the chair remain stationary—the only part of the chair we want to pivot is the center column.

Procedure
● Grab your dumbbells or heavy books.
● Sit in the chair as you would normally.
● Hold one dumbbell or book in each hand, with your arms outstretched.
● Begin your spin in whatever direction you're more comfortable with by kicking off of the ground. You may need to kick off several times. Try to make yourself spin quickly (but safely) while keeping your arms outstretched.
● Once you're spinning freely, pull your books or dumbbells in toward your chest. What happens to the speed of your rotation? Why do you think this is?
●   Reextend your arms outward. What happens to the speed of your rotation this time? Why?

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
Education.com

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