Table of Mechanics Demonstration List of Mechanics Equipment & Supplies Lecture Demonstrations

# Hoberman Sphere, 1Q40.22

Topic and Concept:

Location:

Abstract:

A collapsible sphere suspended from the ceiling is given a spin. A weight attached to the collapse mechanism is dropped causing the sphere to reduce its moment of inertia. Upon collapsing, the rotational speed of the sphere increase showing that angular momentum is conserved.

 Equipment Location ID Number Hoberman Sphere ME, Bay A8, Shelf #4 String ME, Bay A8, Shelf #2 5 kg mass ME, Bay B1, Shelf #1

Important Setup Notes:

• The Hoberman Sphere is fragile! Handle with care.
• The hanging procedure is a little tricky. It may be advisable to contact the lecture demo office ahead of time for tips.
• This demo can only be performed in rooms 2103 and 2241.

Setup and Procedure:

1. For each of the two rooms (2241 & 2103), there is a different string to deal with the difference in ceiling height. Pick the appropriate one.

2. Each full string is composed two individual strings connected with a turnbuckle. On string is connected to a hook and the opposite end of the full string should have a loop. Make a loop if there isn't one (see photos below).
3. On the top of the sphere, there is a pulley (see photos below). Run the loop end of the string through the bottom of the pulley and then through the bottom hole of the turnbuckle.
4. During this step, hold on to the looped end so the previous steps are not undone. Using a long, hooked, wooden rod (located near the back entrance to each room), hook the hook over the D-bracket in the ceiling as shown. The best way to do this is to hook the hook over the hook of the rod, and then balance this as you raise the rod up to the ceiling.
5. Keeping hold of the looped end, walk over to the bracket on the wall (see photos) and hang the loop off the bracket. The sphere should now be suspended.
6. You should see another string hanging through the center of the sphere also with a looped end. This is the collapse string. If pulled, it wall cause the sphere to contract. This is what the 5 kg mass will hang from. Go ahead and loop the loop over the hook on the mass, but DON'T let go of the weight yet.
7. When ready, give the sphere a modest spin (still holding onto the mass).
8. Slowly release the mass while the release string is taught. The sphere will start to increase in rotational speed.

Cautions, Warnings, or Safety Concerns:

• Be careful not to drop the 5 kg mass on your foot...ouch!

Discussion:

For the purposes of this discussion we will consider the open Hoberman Sphere as a thin-walled, hollow sphere of radius Ropen and the closed Hoberman Sphere a solid sphere of radius Rclosed. The moment of inertia of each of these configurations is then

• Iopen = (2/3)*M*Ropen2

• Iclosed = (2/5)*M*Rclosed2

Clearly, since M is constant and Ropen > Rclosed, it follows that Iopen > Iclosed. The magnitude of the angular momentum of the rotating sphere is given by L = I*ω where I is the moment of inertia and ω is the angular speed. Since angular momentum is conserved, when the weight drops causing Iopen to reduce to Iclosed, ω must increase, which is what we observe.

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