Hoberman Sphere, 1Q40.22

Topic and Concept:

• Rotational Dynamics, [:RotationalDynamics#ConsrvationAngMomentum: 1Q40. Conservation of Angular Momentum]

Location:

• Cabinet: [:MechanicsCabinet:Mechanic (ME)]

• Bay: [:MechanicsCabinetBayA8:(A8)]

• Shelf: #4

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.

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 R_open and the closed Hoberman Sphere a solid sphere of radius R_closed. The moment of inertia of each of these configurations is then

• I_open = (2/3)*M*R_open²

• I_closed = (2/5)*M*R_closed²

Clearly, since M is constant and R_open > R_closed, it follows that I_open > I_closed. 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 I_open to reduce to I_closed, ω must increase, which is what we observe.

Videos:

• [https://www.youtube.com/user/LectureDemostrations/videos?view=1 Lecture Demonstration's Youtube Channel]

References:

• [https://en.wikipedia.org/wiki/Hoberman_sphere Wikipedia - Hoberman Sphere]

• [https://en.wikipedia.org/wiki/Angular_momentum Wikipedia - Angular Momentum]

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