Angular Momentum Chair
| Physics, Astronomy: | Momentum, Angular Momentum |
| Grade Range: | Elementary School, Middle School, High School |
| Format: | Hands-on, Stage |
This demonstration is versatile, and is flexible enough to fit into almost any Physics or Astronomy themed show. The topic matter is simple enough for young kids to understand, and it can be applied to much that older students would be learning in class.
Materials
- Hand Weights
- Bike Wheel
- Spinning Stool
Safety Precautions
Please read the Physical Demonstration section of the Demonstration Safety page before performing this demonstration.
Demonstration
- Choose a volunteer from the audience to come and sit on the stool, with their feet on the bar. Give them the hand weights, and instruct them to hold the weights out sideways. Then, after you start spinning them, they are to pull the weights in when you say "GO". Perform the demonstration.
- Now have them do it again, but this time have them start with the weights held to their chest, and on "GO" they extend their arms outward. Thank them for volunteering and have them return to their seat. Explain the first part of the demonstration at this time.
- Choose a new volunteer, someone who can hold the wheel up and away from themselves without the wheel hitting them. Have them sit on the stool, with their feet on the bar, and give them the wheel. Have them try to turn it on its side, to see if they can hold it Point out that, right now, nothing happens when they do that.
- Take the wheel back, and get it spinning quickly. Hand it back to the volunteer and have them turn it on its side again. They will start to spin!
- Thank the volunteer, and have them return to their seat. Explain the demonstration.
Why This Works
Short Explanation
Momentum is when something with mass has a velocity to it. A simple example of this is walking across the floor; when walking at a constant pace, you have momentum. Angular momentum is when you have a mass with velocity, but it is either spinning or moving on a curve. an example would be the feeling you get when you are in a car that goes quickly around a turn. You have momentum while in the car, and when it is turning that momentum is angled. So, you feel what you might think of as a "pull" away from the inside of the turn. This is because momentum is conserved, meaning that it stays at the same amount at all times.
When the volunteer was spinning with the weights held out, the weights had angular momentum to them, and we can think of them drawing a big circle around the volunteer. When they pulled the weights in, the weights now made a smaller circle. If they stayed spinning at the same initial rate, then the weights would be moving much slower in that smaller circle, which would mean that they lost momentum. So in order for momentum to be conserved, the chair started spinning faster! This is true for the opposite as well: When they move the weights outward, they start making a big circle again, so momentum is conserved by them slowing down.
The wheel also uses this idea. When the wheel is spinning vertically, it has momentum along that vertical line. When they turn the wheel sideways, it loses some momentum while changing to the horizontal line, and that momentum goes into the volunteer. Since they are sitting on the stool, the stool will start to spin! The direction they spin in is related to the direction that the wheel is spinning. This means that, if you took the wheel, turned it around, and gave it back, that they would then spin in the opposite direction when they turn it!
Full Explanation
Momentum is when a mass has a constant velocity, meaning that it has zero acceleration. This type of momentum we can think of being linear, or traveling along a single dimensional line (typically the x-axis). When an object is changing the direction of its velocity, it will experience Angular Momentum. This introduces a second, distance variable, which changes in relation to the velocity variable as the object rotates around a fixed axial point. Angular Momentum can also be seen in a third dimensional view, where the momentum of the system can be viewed based on the rotation of the two-dimensional system as a whole along a third axis, which allows the momentum to be transferred from one plane of rotation to another. In other words:
| Linear Momentum (One-Dimensional) | Angular Momentum (Two-Dimensional) | Angular Momentum (Three-Dimensional) |
| p = m*v | ∫ p dr = m*v*r | ∫ ∫ p dr dθ = m*v*r*sin(θ) + m*v*r*cos(θ) |
| Changes in the x-axis | Changes in the x- AND y-axis | Changes in the x- AND y-axis, angled to the z-axis |
Where p = Momentum (constant), m = Mass (constant), v = Velocity (variable), r = Radius of Rotation (variable), and θ = Angle to the z-axis (variable)
When the volunteer is holding the weights, we are looking at the two-dimensional representation of Angular Momentum. The center of the chair is where the radius of rotation is based, so the starting distance of the weights will determine the initial rotational radius. When they move the weights to the new radius, the change in radius (r) will cause a proportional change in velocity (v) in order to keep the momentum of the system conserved, resulting in the p value being unchanged.
When we introduce the wheel, we are seeing a change happen now in three dimensions. The wheel, while spinning, has a set momentum, with the velocity, mass and radius all being constant. However, when the wheel is rotated along the z-axis, we see that the momentum value stays unchanged, since it transfers between sine and cosine. When the wheel is held straight by the volunteer, the momentum is completely within a two-dimensional plane. When we turn the wheel on its side, it is now on a different two-dimensional plane, and causes a transfer from the sin(θ) to the cos(θ) in the equation above. To create this transfer, you need to put momentum into the system, and since the momentum in the system must be conserved, that addition will come out of the system into you, causing you to spin.
Another way to think of why you spin is by using the Right Hand Rule. Place your thumb along the axis of rotation for the wheel, and your fingers will face outward with the wheel, and curl over in the direction of rotation. When you turn your hand so your thumb is now facing upwards, the rotation of the wheel will be along the horizontal plane, and the rotation of the stool will be the opposite of the rotation of the wheel. This is because of the Conservation of Angular Momentum: the momentum of the system must stay conserved, so you cannot add or subtract from it. Therefore, since you have to apply a force upon the wheel to make it rotate between the horizontal and vertical planes, the resulting momentum that would be placed on the wheel must be opposed, and is put back into you, and therefore the stool.
Additional Information
- Make sure to reference real-life examples of this concept in use, such as figure skating, planetary orbits, the length of the day, or spinning tops!
- This demonstration is a part of the Astronomy Show.