How Do You Calculate the Torsional Constant of a Wire?

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In summary, the torsional constant of the wire can be calculated using the formula k=(w^2)(I), where w is the angular frequency and I is the rotational inertia of the hollow ball.
  • #1
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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  • #2
do i have to use the rotational inertia of the hollow sphere? 2/3 M R^2 ??
 
  • #3
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.
 
  • #4
as time... wouldn't it be something as Acoswt ?
 
  • #5
i already solved it! thanks! it was using this k=(w^2 )(I)
 

Related to How Do You Calculate the Torsional Constant of a Wire?

1. What is a torsional hollow ball?

A torsional hollow ball is a spherical object with an empty interior that is designed to rotate or twist along its axis.

2. How is a torsional hollow ball different from a regular ball?

A regular ball is typically solid and does not have the ability to rotate or twist along its axis, whereas a torsional hollow ball is specifically designed for this purpose.

3. What is the scientific principle behind the function of a torsional hollow ball?

The function of a torsional hollow ball is based on the physical property of torsion, which is the twisting or rotating force applied to an object.

4. What are some potential applications of a torsional hollow ball?

Torsional hollow balls can be used in various applications, such as in mechanical systems to transfer rotational motion, in gyroscopes for navigation and stabilization, and in torsion balance experiments to measure torque and angular acceleration.

5. How is a torsional hollow ball made?

Torsional hollow balls are typically made from a variety of materials such as metal, plastic, or rubber, and are often manufactured using a molding or casting process. The design of the hollow interior may vary depending on the intended application of the ball.

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