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torsional stiffness is the ability of an object to resist twisting when acted upon by an external force, torque. Check FAQs
q=(2⋅π)2⋅Id(tp)2
q - Torsional Stiffness?Id - Mass Moment of Inertia of Disc?tp - Time Period?π - Archimedes' constant?

Torsional Stiffness of Shaft given Time Period of Vibration Example

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Here is how the Torsional Stiffness of Shaft given Time Period of Vibration equation looks like with Values.

Here is how the Torsional Stiffness of Shaft given Time Period of Vibration equation looks like with Units.

Here is how the Torsional Stiffness of Shaft given Time Period of Vibration equation looks like.

5.4Edit=(2⋅3.1416)2⋅6.2Edit(6.7325Edit)2
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HomeIcon Home » Category Physics » Category Mechanical » Category Theory of Machine » fx Torsional Stiffness of Shaft given Time Period of Vibration

Torsional Stiffness of Shaft given Time Period of Vibration Solution

Follow our step by step solution on how to calculate Torsional Stiffness of Shaft given Time Period of Vibration?

FIRST Step Consider the formula
q=(2⋅π)2⋅Id(tp)2
Next Step Substitute values of Variables
∴ q=(2⋅π)2⋅6.2kg·m²(6.7325s)2
Next Step Substitute values of Constants
∴ q=(2⋅3.1416)2⋅6.2kg·m²(6.7325s)2
Next Step Prepare to Evaluate
∴ q=(2⋅3.1416)2⋅6.2(6.7325)2
Next Step Evaluate
∴q=5.400000012306N/m
LAST Step Rounding Answer
∴q=5.4N/m

Torsional Stiffness of Shaft given Time Period of Vibration Formula Elements

Variables
Constants
Torsional Stiffness
torsional stiffness is the ability of an object to resist twisting when acted upon by an external force, torque.
Symbol: q
Measurement: Stiffness ConstantUnit: N/m
Note: Value should be greater than 0.
Formulas to find Torsional StiffnessOpen Variable
Mass Moment of Inertia of Disc
Mass Moment of Inertia of Disc is the rotational inertia of a disc that resists changes in its rotational motion, used in torsional vibration analysis.
Symbol: Id
Measurement: Moment of InertiaUnit: kg·m²
Note: Value should be greater than 0.
Formulas to find Mass Moment of Inertia of DiscOpen Variable
Time Period
Time Period is the time taken by the shaft to complete one oscillation or vibration about its axis in a torsional vibration system.
Symbol: tp
Measurement: TimeUnit: s
Note: Value should be greater than 0.
Formulas to find Time PeriodOpen Variable
Archimedes' constant
Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.
Symbol: π
Value: 3.14159265358979323846264338327950288

Other Formulas to find Torsional Stiffness

​Go Torsional Stiffness of Shaft given Natural Frequency of Vibration
q=(2⋅π⋅fn)2⋅Id
​Go Torsional Stiffness of Shaft
q=Frθ

Other formulas in Natural Frequency of Free Torsional Vibrations category

​Go Moment of Inertia of Disc using Natural Frequency of Vibration
Id=q(2⋅π⋅fn)2
​Go Moment of Inertia of Disc given Time Period of Vibration
Id=tp2⋅q(2⋅π)2
​Go Time Period for Vibrations
tp=2⋅π⋅Idq
​Go Moment of Inertia of Disc given Angular Velocity
Id=qrω2

How to Evaluate Torsional Stiffness of Shaft given Time Period of Vibration?

Torsional Stiffness of Shaft given Time Period of Vibration evaluator uses Torsional Stiffness = ((2*pi)^2*Mass Moment of Inertia of Disc)/(Time Period)^2 to evaluate the Torsional Stiffness, Torsional Stiffness of Shaft given Time Period of Vibration formula is defined as the measure of a shaft's resistance to twisting forces, which is essential in determining the shaft's ability to withstand torsional vibrations, and is a critical parameter in the design and analysis of rotating machines and mechanical systems. Torsional Stiffness is denoted by q symbol.

How to evaluate Torsional Stiffness of Shaft given Time Period of Vibration using this online evaluator? To use this online evaluator for Torsional Stiffness of Shaft given Time Period of Vibration, enter Mass Moment of Inertia of Disc (Id) & Time Period (tp) and hit the calculate button.

FAQs on Torsional Stiffness of Shaft given Time Period of Vibration

What is the formula to find Torsional Stiffness of Shaft given Time Period of Vibration?
The formula of Torsional Stiffness of Shaft given Time Period of Vibration is expressed as Torsional Stiffness = ((2*pi)^2*Mass Moment of Inertia of Disc)/(Time Period)^2. Here is an example- 5.4 = ((2*pi)^2*6.2)/(6.7325383)^2.
How to calculate Torsional Stiffness of Shaft given Time Period of Vibration?
With Mass Moment of Inertia of Disc (Id) & Time Period (tp) we can find Torsional Stiffness of Shaft given Time Period of Vibration using the formula - Torsional Stiffness = ((2*pi)^2*Mass Moment of Inertia of Disc)/(Time Period)^2. This formula also uses Archimedes' constant .
What are the other ways to Calculate Torsional Stiffness?
Here are the different ways to Calculate Torsional Stiffness-
  • Torsional Stiffness=(2*pi*Natural Frequency)^2*Mass Moment of Inertia of DiscOpenImg
  • Torsional Stiffness=Restoring Force/Angular Displacement of ShaftOpenImg
Can the Torsional Stiffness of Shaft given Time Period of Vibration be negative?
No, the Torsional Stiffness of Shaft given Time Period of Vibration, measured in Stiffness Constant cannot be negative.
Which unit is used to measure Torsional Stiffness of Shaft given Time Period of Vibration?
Torsional Stiffness of Shaft given Time Period of Vibration is usually measured using the Newton per Meter[N/m] for Stiffness Constant. Newton per Millimeter[N/m], Kilonewton per Millimeter[N/m] are the few other units in which Torsional Stiffness of Shaft given Time Period of Vibration can be measured.
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