### An engaging demonstration of conservation of angular momentum.

Watch The Video:

Teachable Topics:

• Angular speed
• Rotational inertia
• Conservation of momentum

Theory:

The conservation of momentum states that the momentum, including angular momentum, must remain constant. Angular momentum is given by the following formula:

L = Iω

where L is angular momentum, I is the moment of inertia, and ω is the angular velocity.

Since this value must be conserved, the initial value of L for the system, (in this case the stool, the student, and the weights) must be the same as the final value.

The student sitting on the stool in this demonstration can be approximated as a cylinder of mass M and radius R, which then has a rotational inertia of MR2/2. For the initial condition of the student holding the weights (of mass, m) out, the rotational inertia of the weights must be added to that of the cylinder to get the total initial rotational inertia. When the weights are brought in to the student’s center, the rotational inertia is only that of the cylinder with a slightly increased mass: (2m + M)R2/2. This inertia is still less than that of the initial condition so the angular speed must increase when the weights are brought close to the body to keep the value of angular momentum constant. In other words, the speed of the spinning student goes up!

Apparatus:

• Stool that spins well and has a foot rest
• Two weights (light enough for a student to hold them out at arms length)
• A student willing to be spun (works best with a light student!)

Procedure:

• Have the willing student sit on the stool and hand them the two weights.
• Have the student hold one weight in each hand and hold their arms straight out to their sides.
• Give the student a decent spin while the student continues to hold the weights out.
• Tell the student to bring in their arms and albows and hold their hands and the weights at their chest.
• After the student has sped up, have them put thir arms back out at their sides to slow down again. This can be repeated until the student comes to a stop.

SAFETY WARNINGS:

• Most students are initially surprised at the quick increase in speed they feel when pulling their arms in. It may take a practice spin for them to get used to the feeling and to know they won't fall off!
• Don't spin the student too fast.