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Moment of Inertia of Shaft given Circular Frequency Calculator

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General Shaft Shaft Fixed at Both Ends Carrying a Uniformly Distributed Load Shaft Subjected to a Number of Point Loads Uniformly Distributed Load Acting Over a Simply Supported Shaft

✖Natural Circular Frequency is a scalar measure of rotation rate.ⓘ Natural Circular Frequency [ω_n]			+10% -10%
✖Load per unit length is the distributed load which is spread over a surface or line.ⓘ Load per unit length [w]			+10% -10%
✖Length of shaft is the distance between two ends of shaft.ⓘ Length of Shaft [L_shaft]			+10% -10%
✖Young's Modulus is a mechanical property of linear elastic solid substances. It describes the relationship between longitudinal stress and longitudinal strain.ⓘ Young's Modulus [E]			+10% -10%
✖Acceleration due to Gravity is acceleration gained by an object because of gravitational force.ⓘ Acceleration due to Gravity [g]			+10% -10%

✖Moment of inertia of shaft can be calculated by taking the distance of each particle from the axis of rotation.ⓘ Moment of Inertia of Shaft given Circular Frequency [I_shaft]

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Moment of Inertia of Shaft given Circular Frequency Solution

STEP 0: Pre-Calculation Summary

Formula Used

Moment of inertia of shaft = (Natural Circular Frequency^2*Load per unit length*(Length of Shaft^4))/(pi^4*Young's Modulus*Acceleration due to Gravity)
I_shaft = (ω_n^2*w*(L_shaft^4))/(pi^4*E*g)
This formula uses 1 Constants, 6 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Moment of inertia of shaft - (Measured in Kilogram Square Meter) - Moment of inertia of shaft can be calculated by taking the distance of each particle from the axis of rotation.
Natural Circular Frequency - (Measured in Radian per Second) - Natural Circular Frequency is a scalar measure of rotation rate.
Load per unit length - Load per unit length is the distributed load which is spread over a surface or line.
Length of Shaft - (Measured in Meter) - Length of shaft is the distance between two ends of shaft.
Young's Modulus - (Measured in Newton per Meter) - Young's Modulus is a mechanical property of linear elastic solid substances. It describes the relationship between longitudinal stress and longitudinal strain.
Acceleration due to Gravity - (Measured in Meter per Square Second) - Acceleration due to Gravity is acceleration gained by an object because of gravitational force.

STEP 1: Convert Input(s) to Base Unit

Natural Circular Frequency: 13.1 Radian per Second --> 13.1 Radian per Second No Conversion Required
Load per unit length: 3 --> No Conversion Required
Length of Shaft: 3.5 Meter --> 3.5 Meter No Conversion Required
Young's Modulus: 15 Newton per Meter --> 15 Newton per Meter No Conversion Required
Acceleration due to Gravity: 9.8 Meter per Square Second --> 9.8 Meter per Square Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

I_shaft = (ω_n^2*w*(L_shaft^4))/(pi^4*E*g) --> (13.1^2*3*(3.5^4))/(pi^4*15*9.8)

Evaluating ... ...

I_shaft = 5.39534472009954

STEP 3: Convert Result to Output's Unit

5.39534472009954 Kilogram Square Meter --> No Conversion Required

FINAL ANSWER

5.39534472009954 ≈ 5.395345 Kilogram Square Meter <-- Moment of inertia of shaft

(Calculation completed in 00.004 seconds)

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Home » Physics » Theory of Machine » Vibrations » Longitudinal and Transverse Vibrations » Mechanical » Natural Frequency of Free Transverse Vibrations » Moment of Inertia of Shaft given Circular Frequency

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National Institute Of Technology (NIT), Hamirpur

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< Natural Frequency of Free Transverse Vibrations Calculators

Length of Shaft

Go Length of Shaft = ((Static Deflection*3*Young's Modulus*Moment of inertia of shaft)/(Load Attached to Free End of Constraint))^(1/3)

Static Deflection given Moment of Inertia of Shaft

Go Static Deflection = (Load Attached to Free End of Constraint*Length of Shaft^3)/(3*Young's Modulus*Moment of inertia of shaft)

Moment of Inertia of Shaft given Static Deflection

Go Moment of inertia of shaft = (Load Attached to Free End of Constraint*Length of Shaft^3)/(3*Young's Modulus*Static Deflection)

Load at Free End in Free Transverse Vibrations

Go Load Attached to Free End of Constraint = (Static Deflection*3*Young's Modulus*Moment of inertia of shaft)/(Length of Shaft^3)

Moment of Inertia of Shaft given Circular Frequency Formula

Moment of inertia of shaft = (Natural Circular Frequency^2*Load per unit length*(Length of Shaft^4))/(pi^4*Young's Modulus*Acceleration due to Gravity)
I_shaft = (ω_n^2*w*(L_shaft^4))/(pi^4*E*g)

What is transverse and longitudinal vibration?

The difference between transverse and longitudinal waves is the direction in which the waves shake. If the wave shakes perpendicular to the movement direction, it's a transverse wave, if it shakes in the movement direction, then it's a longitudinal wave.

How to Calculate Moment of Inertia of Shaft given Circular Frequency?

Moment of Inertia of Shaft given Circular Frequency calculator uses Moment of inertia of shaft = (Natural Circular Frequency^2*Load per unit length*(Length of Shaft^4))/(pi^4*Young's Modulus*Acceleration due to Gravity) to calculate the Moment of inertia of shaft, Moment of Inertia of Shaft given Circular Frequency formula is defined as a measure of the shaft's resistance to changes in its rotational motion, which is essential in determining the natural frequency of free transverse vibrations in mechanical systems, particularly in the design of rotating machinery and structures. Moment of inertia of shaft is denoted by I_shaft symbol.

How to calculate Moment of Inertia of Shaft given Circular Frequency using this online calculator? To use this online calculator for Moment of Inertia of Shaft given Circular Frequency, enter Natural Circular Frequency (ω_n), Load per unit length (w), Length of Shaft (L_shaft), Young's Modulus (E) & Acceleration due to Gravity (g) and hit the calculate button. Here is how the Moment of Inertia of Shaft given Circular Frequency calculation can be explained with given input values -> 5.395345 = (13.1^2*3*(3.5^4))/(pi^4*15*9.8).

FAQ

What is Moment of Inertia of Shaft given Circular Frequency?

Moment of Inertia of Shaft given Circular Frequency formula is defined as a measure of the shaft's resistance to changes in its rotational motion, which is essential in determining the natural frequency of free transverse vibrations in mechanical systems, particularly in the design of rotating machinery and structures and is represented as I_shaft = (ω_n^2*w*(L_shaft^4))/(pi^4*E*g) or Moment of inertia of shaft = (Natural Circular Frequency^2*Load per unit length*(Length of Shaft^4))/(pi^4*Young's Modulus*Acceleration due to Gravity). Natural Circular Frequency is a scalar measure of rotation rate, Load per unit length is the distributed load which is spread over a surface or line, Length of shaft is the distance between two ends of shaft, Young's Modulus is a mechanical property of linear elastic solid substances. It describes the relationship between longitudinal stress and longitudinal strain & Acceleration due to Gravity is acceleration gained by an object because of gravitational force.

How to calculate Moment of Inertia of Shaft given Circular Frequency?

Moment of Inertia of Shaft given Circular Frequency formula is defined as a measure of the shaft's resistance to changes in its rotational motion, which is essential in determining the natural frequency of free transverse vibrations in mechanical systems, particularly in the design of rotating machinery and structures is calculated using Moment of inertia of shaft = (Natural Circular Frequency^2*Load per unit length*(Length of Shaft^4))/(pi^4*Young's Modulus*Acceleration due to Gravity). To calculate Moment of Inertia of Shaft given Circular Frequency, you need Natural Circular Frequency (ω_n), Load per unit length (w), Length of Shaft (L_shaft), Young's Modulus (E) & Acceleration due to Gravity (g). With our tool, you need to enter the respective value for Natural Circular Frequency, Load per unit length, Length of Shaft, Young's Modulus & Acceleration due to Gravity and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Moment of inertia of shaft?

In this formula, Moment of inertia of shaft uses Natural Circular Frequency, Load per unit length, Length of Shaft, Young's Modulus & Acceleration due to Gravity. We can use 3 other way(s) to calculate the same, which is/are as follows -

Moment of inertia of shaft = (Load Attached to Free End of Constraint*Length of Shaft^3)/(3*Young's Modulus*Static Deflection)
Moment of inertia of shaft = (Load per unit length*Length of Shaft^4)/(384*Young's Modulus*Static Deflection)
Moment of inertia of shaft = (Frequency^2*Load per unit length*Length of Shaft^4)/(3.573^2*Young's Modulus*Acceleration due to Gravity)

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