For our dynamic measurement of the moment of inertia, we will use a vertically-mounted turntable that has a hub attached at its center, which has three grooves of different radius, around which one can wind a string. A mass hanging from the free end of the string provides tension, which exerts a torque on the turntable, thus causing it to rotate. By measuring the time it takes the mass to fall from its initial height to the table top (or some reference line just above it), we can find aa, its (linear) acceleration. From this we can calculate αα, the angular acceleration of the turntable. From the weight of the mass, and its linear acceleration, we can find T, the tension in the string. Once we know all these things, we can calculate the torque, ττ, and from τ=Iατ=Iα find I, the moment of inertia of our turntable platter. Assumptions made in this experiment:  - Turntable disk mass/density was distributed evenly (this is not the case, it is actually concentrated in center) - Assumed that there was a central axis of rotation on the disk (this might not be the case, as central axis could have been offset accidentally). In what way could these assumptions cause a discrepancy between the accepted and experimental values obtained for the moment of inertia?

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For our dynamic measurement of the moment of inertia, we will use a vertically-mounted turntable that has a hub attached at its center, which has three grooves of different radius, around which one can wind a string. A mass hanging from the free end of the string provides tension, which exerts a torque on the turntable, thus causing it to rotate. By measuring the time it takes the mass to fall from its initial height to the table top (or some reference line just above it), we can find aa, its (linear) acceleration. From this we can calculate αα, the angular acceleration of the turntable. From the weight of the mass, and its linear acceleration, we can find T, the tension in the string. Once we know all these things, we can calculate the torque, ττ, and from τ=Iατ=Iα find I, the moment of inertia of our turntable platter.

Assumptions made in this experiment: 

- Turntable disk mass/density was distributed evenly (this is not the case, it is actually concentrated in center)

- Assumed that there was a central axis of rotation on the disk (this might not be the case, as central axis could have been offset accidentally).

  1. In what way could these assumptions cause a discrepancy between the accepted and experimental values obtained for the moment of inertia?

T
a
m
mg
Figure 5
Transcribed Image Text:T a m mg Figure 5
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