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# Hoberman Sphere, 1Q40.22

Topic and Concept:

Location:

attachment:Hoberman16-400.jpg

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 [:MechanicsCabinetBayA8: ME, Bay A8, Shelf #4] String [:MechanicsCabinetBayA8: ME, Bay A8, Shelf #2] 5 kg mass [:MechanicsCabinetBayB1: ME, Bay B1, Shelf #1]

Important Setup Notes:

• The Hoberman Sphere is fragile! Handle with care.

Setup and Procedure:

1. List steps for setup then procedure.
2. ...

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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