How Do You Calculate the Torsional Constant of a Wire?

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SUMMARY

The torsional constant of a wire can be calculated using the formula k = ω²I, where ω is the angular frequency and I is the rotational inertia. In this discussion, a 560 g hollow ball with a diameter of 18 cm oscillates at a frequency of 0.78 Hz. The rotational inertia for the hollow sphere is determined using the formula I = (2/3)MR². By substituting the calculated values into the equation, the torsional constant is successfully derived.

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  • Understanding of torsional oscillations
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  • Knowledge of rotational inertia for hollow spheres
  • Proficiency in applying physics equations related to torque and angular motion
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  • Learn how to derive the angular frequency from oscillation frequency
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Students in physics, mechanical engineers, and anyone interested in the dynamics of torsional systems will benefit from this discussion.

Robertoalva
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1. A 560 g hollow ball 18 cm in diameter is suspended by a wire and is undergoing torsional oscillations at a frequency of 0.78 Hz. What is the torsional constant of the wire?



Homework Equations


F=-κθ
ω=sqrt(κ/I)

The Attempt at a Solution


tried to use the frequency to get the angular displacement and then just solve for k but I didn't get the answer
 
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do i have to use the rotational inertia of the hollow sphere? 2/3 M R^2 ??
 
Robertoalva said:
1. A 560 g hollow ball 18 cm in diameter is suspended by a wire and is undergoing torsional oscillations at a frequency of 0.78 Hz. What is the torsional constant of the wire?

Homework Equations


F=-κθ
ω=sqrt(κ/I)

The Attempt at a Solution


tried to use the frequency to get the angular displacement and then just solve for k but I didn't get the answer
Can you write the angular displacement of the ball as a function of time ?

Robertoalva said:
do i have to use the rotational inertia of the hollow sphere? 2/3 M R^2 ??
Yes. You will need that.
 
as time... wouldn't it be something as Acoswt ?
 
i already solved it! thanks! it was using this k=(w^2 )(I)
 

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