Angular Momentum Chair: Difference between revisions

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== Age ==
{| class="wikitable" style="color:black; background-color:#ddd; margin-left: auto; float:right"
| [[Physics]], [[Astronomy]]:
| Momentum, Angular Momentum
|-
| Grade Range:
| [[Elementary School]], [[Middle School]], [[High School]]
|-
| Format:
| [[Hands-on]], [[Stage]]
|}


Elementary School,Middle School,High School
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.
 
== Format ==
 
Stage Show,Hands-on
 
== Scientific Concepts ==
 
Angular momentum and conservation of momentum


== Materials ==
== Materials ==


    Small dumbbells
* Hand Weights
    Spinning chair
* Bike Wheel
    Bike wheel on mount
* Spinning Stool
    Also see chart attached to box!


== Safety Precautions ==
== Safety Precautions ==


Science Theatre demonstrators must keep the safety of themselves and their audience in mind at all times. All Science Theatre demonstrators must have read through the Safety Training page. The ST Safety Box with first aid kit, fire extinguisher, etc. should always be available to demonstrators. Always wear safety gloves, glasses, and a labcoat if handling chemicals; always perform potentially dangerous demonstrations at a safe distance from the audience; and always keep a very close eye on any volunteers you call from the audience. Dizziness and potential flying weights. Don't spin kids too fast and keep a small radius clear of viewers in case weight gets dropped.
Please read the Physical Demonstration section of the [[Demonstration Safety]] page before performing this demonstration.


== Preparation ==  
== Demonstration ==


Sturdy ground and a couple of volunteers
# 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.


== Demonstration ==
== Why This Works ==


After the intro talk, have a volunteer sit on the chair. Have the seated volunteer hold one weight in each hand. While spinning, have the volunteer slowly extend their arms outward with the weights. Observe decrease in revolutions per minute. Bring weights back in. Observe increase in revolutions per minute. Stop Chair and discuss observations. Have another volunteer sit on chair. Spin the bike wheel and hand it to the volunteer vertically. Have the volunteer move the wheel so it is horizontal. Observe that the person starts spinning. Have the volunteer switch the wheel's rotation (flip it 180 degrees). Observe the chair slow, stop, and revers. Have the volunteer return the wheel to its upright position, take wheel from the volunteer and have them return to their seat. Stop wheel and discuss with observers.
===Short Explanation===


== What to Say ==
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.


Start by discussing momentum in linear paths.
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.
Example. "So have you ever noticed how things are moving tend to be very hard to stop? This property of matter is call inertia or momentum, a body's ability to resist change in motion. Momentum, quantitatively, is the product of mass and velocity, So a heavier thing moving quickly will have much more momentum than something lighter moving at the same speed."


Explain conservation of momentum.
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!
Example. "So you guys know that mass is conserved in systems right? If I take a 5 kilogram weight and break it into pieces, all the pieces will add to be 5 kilograms. Well, the same goes for momentum. If a system of several objects has a certain amount of momentum, it will always maintain that same amount of momentum - even if it gets redistributed amongst the objects in the system. External forces like friction and air resistance can change the amount of momentum in a system."
You can use the example of a simple collusion between billiard balls, where momentum is transferred and conserved. Note that this type of momentum is 'linear' momentum - the balls move in straight lines.


Relate momentum and its conservation to rotational system. \\ Example. "So we understand how momentum works in straight lines right? Well it works the same when things spin too. Something at a certain speed, measured in RPMs, will keep that speed unless something comes to take it away. Now, with things that rotate we have a couple other nest things with momentum. For instance, the distance away from the axis of rotation (what the object spins around) can change the way things rotate. Specifically, we'll talk about moments of inertia. That's a big physics term that basically says, 'for round objects, the farther away from the middle the weight is, the slower it will want to move.' So a hallow ball will spin much slower than a solid ball if they have the same mass."
===Full Explanation===


Bring out the chair!
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:
Example. "So I've got a little demo here to help you guys see momentum in action. Let's pretend this chair is an isolated system. (Get two volunteers and lean their names) SO I'm going to have (Volunteer 1) sit here on the chair and spin. Look at him/her go. Now assuming nothing comes along to stop her, (Volunteer 1) will spin like this forever and ever. But we like (Volunteer 1) so we'll let her put her feet down to stop. Now, to show you a little about those 'moments of inertia' I'm going to give (Volunteer 1) a couple of weights. Careful now, they are weights. Ok, so let's start off with weights clase to you. (Start spinning) Ok, now what I want you to do is slowly take the weights and bring them outward. Ok, bring them back in, and now back out again. Did you guys notice anything? That's right, she slowed down. That's why whenever people spin quickly they try to curl up as tight as possible, like figure skaters or divers."


"Ok (Volunteer 1), thank you very much you may go back to your seat. Let's hear it for (Volunteer 1)! Alrighty, for my next trick, I will have (Volunteer 2) sit on the chair without spinning it. Remember how when (Volunteer 1) brought the weights out the chair slowed down? Well this next part will show this property more clearly. So I've got this bike wheel here and it spins. Now what I'm going to do is start it spinning and hand it to (Volunteer 2) here vertically. Notice that the wheel is spinning vertically and (Volunteer 2) is stationary - no part of the system is spinning in the horizontal direction! Ok (Volunteer 2), turn the wheel now to one side. Now the wheel is spinning horizontally in one direction. Since the original system was not spinning horizontally, by conservation of angular momentum, the systems should never spinning horizontally! That's why (Volunteer 2) starts spinning horizontally in the other direction - to cancel out the spin of the wheel. Ok, now turn it over to the other side. For the same reason, (Volunteer 2) starts spinning in the other direction. Pretty cool stuff eh?"
{| class="wikitable" style="color:black; background-color:#ddd; text-align: center; margin: auto"
| Linear Momentum (One-Dimensional)
| Angular Momentum (Two-Dimensional)
| Angular Momentum (Three-Dimensional)
|-
| ''p'' = m*'''v'''
| '''∫''' ''p'' d'''r''' = m*'''v'''*'''r'''
| '''∫''' '''∫''' ''p'' d'''r''' d'''θ''' = 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
|}


Feel free to insert additional life examples where ever you see fit.
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.


== Why It Is ==
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.


Momentum is conserve in any isolated (closed) system, where there are no net external forces acting (i.e., no friction, gravitation, etc.). This is a fundamental property of the natural world (a law of physics).
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.
Additionally, a neat tid-bit is that Newton derived his second law for momentum. That is , "forced is the rate of change of momentum" is equivalent to 'F-ma.' So Newton's third law is really describing the conservation of momentum, that the interaction of objects yield equal and opposite reactions and thus no net change of momentum.


== Real Life Examples ==
== Additional Information ==


Figure skating, divers, anything that spins
* 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]].

Latest revision as of 22:59, 14 October 2015

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

  1. 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.
  2. 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.
  3. 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.
  4. 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!
  5. 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.
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