Derivation of torsion equations

In summary, for a lab involving a torsional pendulum, the student is given the equation C=(32LQ)/(\pid^4) to use but is required to look up the derivation of this formula due to not covering torsion. The formula for Q is Q=[(2\pi)^2]*[I/(T^2)] where Q is the torsion constant, I is the moment of inertia, and T is the period. However, further information on torsional pendulums was not found in the textbook or online. An example lab report and a professional explanation of torsional pendulums can be found at the link provided.
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Homework Statement


This is for a lab involving a torsional pendulum. We are given the equation below to use, but having not covered torsion, the lab manual says that "The student should look up the derivation of this formula."


Homework Equations


The equation we're asked to find the derivation for is:

C=(32LQ)/([tex]\pi[/tex]d^4)

where C is the torsion modulus of the rod, Q is the torsion constant of the rod, L is the length of the rod, and d is the diameter of the rod.


The Attempt at a Solution



I have already derived the formula Q=[(2[tex]\pi[/tex])^2]*[I/(T^2)]

where Q is the torsion constant of the pendulum's rod, I is the moment of inertia of the object on the pendulum, and T is its period, but I've been entirely unable to find anything further in my book or on the internet.
 
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Related to Derivation of torsion equations

1. What is torsion in the context of engineering and mechanics?

Torsion is a type of stress or force that occurs when a material is twisted or rotated about its axis. It is commonly seen in engineering and mechanics, especially in structures like beams, shafts, and bridges.

2. Why is it important to derive torsion equations?

Deriving torsion equations allows us to understand and predict the behavior of materials under torsional stress. This is crucial in designing structures and machines that can withstand torsional loads without failing.

3. How are torsion equations derived?

Torsion equations are derived using principles of mechanics, specifically the concept of torque and the relationship between shear stress and shear strain. The equations are then applied to different types of materials to determine their torsional behavior.

4. What are the assumptions made in deriving torsion equations?

Some of the common assumptions made in deriving torsion equations include: the material is homogeneous and isotropic, the cross-section remains planar and unchanged during torsion, and the shear stress is distributed uniformly across the cross-section.

5. Are there any limitations to the use of torsion equations?

Yes, torsion equations have limitations and may not accurately predict the behavior of materials in all situations. They are based on certain assumptions and may not account for factors like material defects or complex loading conditions. It is important to use them with caution and consider other factors in engineering design.

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