Torsion Pendulum, 3A10.30

Topic and Concept:

• Oscillations, [:Oscillations#Pendula: 3A10. Pendula]

Location:

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

• Bay: [:MechanicsCabinetBayA12:(A12)]

• Shelf: #T

attachment:TorsionPendulum01-400.jpg

Abstract:

Weight is added to a torsion pendulum to decrease the period of oscillations.

Important Setup Notes:

• N/A

Setup and Procedure:

1. Place the apparatus on the lecture bench.
2. Displace the orange "flag" in a circular direction horizontally and release.
3. Add one of the weights (grey or yellow) to the flag as pictured below and and again set the flag into oscillatory motion. Note the difference in the period of oscillation for each configuration.

Cautions, Warnings, or Safety Concerns:

• N/A

Discussion:

In a torsion pendulum, the restoring force is provided by the torsion in the wire that the mass is connected to. The period of oscillation is dependent upon the moment of inertia of the system and the torsion spring constant of the wire (assuming very little dampening). Mathematically, the period is given by

T = 2π * Sqrt[I/κ] ≈ 2π * R * Sqrt[M/κ]

where I is the moment of inertia, κ is the torsion spring constant, M is the mass of our "bob", and R is the radial distance of the mass from the wire. For our system, the torsion spring constant is constant throughout the demonstration. The distance of the mass from the wire is constant. Thus, when we add mass to the system, I is increased resulting in an increase in the period of oscillation.

Videos:

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

References:

• [https://en.wikipedia.org/wiki/Oscillation Wikipedia - Oscillation]

• [https://en.wikipedia.org/wiki/Pendulum Wikipedia - Pendulum]

• [https://en.wikipedia.org/wiki/Torsion_pendulum#Torsion_balance Wikipedia - Torsion Pendulum]

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