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Moment of Inertia of Shaft given Circular Frequency Calculator

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

✖Natural Circular Frequency is the number of oscillations per unit time of a system vibrating freely in transverse mode without any external force.ⓘ Natural Circular Frequency [ω_n]			+10% -10%
✖Load per unit length is the force per unit length applied to a system, affecting its natural frequency of free transverse vibrations.ⓘ Load per unit length [w]			+10% -10%
✖Length of Shaft is the distance from the axis of rotation to the point of maximum vibration amplitude in a transversely vibrating shaft.ⓘ Length of Shaft [L_shaft]			+10% -10%
✖Young's Modulus is a measure of the stiffness of a solid material and is used to calculate the natural frequency of free transverse vibrations.ⓘ Young's Modulus [E]			+10% -10%
✖Acceleration due to Gravity is the rate of change of velocity of an object under the influence of gravitational force, affecting natural frequency of free transverse vibrations.ⓘ Acceleration due to Gravity [g]			+10% -10%

✖Moment of inertia of shaft is the measure of an object's resistance to changes in its rotation, influencing natural frequency of free transverse vibrations.ⓘ 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 is the measure of an object's resistance to changes in its rotation, influencing natural frequency of free transverse vibrations.
Natural Circular Frequency - (Measured in Radian per Second) - Natural Circular Frequency is the number of oscillations per unit time of a system vibrating freely in transverse mode without any external force.
Load per unit length - Load per unit length is the force per unit length applied to a system, affecting its natural frequency of free transverse vibrations.
Length of Shaft - (Measured in Meter) - Length of Shaft is the distance from the axis of rotation to the point of maximum vibration amplitude in a transversely vibrating shaft.
Young's Modulus - (Measured in Newton per Meter) - Young's Modulus is a measure of the stiffness of a solid material and is used to calculate the natural frequency of free transverse vibrations.
Acceleration due to Gravity - (Measured in Meter per Square Second) - Acceleration due to Gravity is the rate of change of velocity of an object under the influence of gravitational force, affecting natural frequency of free transverse vibrations.

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 » Natural Frequency of Free Transverse Vibrations » Mechanical » Uniformly Distributed Load Acting Over a Simply Supported Shaft » Moment of Inertia of Shaft given Circular Frequency

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National Institute Of Technology (NIT), Hamirpur

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< Uniformly Distributed Load Acting Over a Simply Supported Shaft Calculators

Length of Shaft given Static Deflection

LaTeX Go Length of Shaft = ((Static Deflection*384*Young's Modulus*Moment of inertia of shaft)/(5*Load per unit length))^(1/4)

Uniformly Distributed Load Unit Length given Static Deflection

LaTeX Go Load per unit length = (Static Deflection*384*Young's Modulus*Moment of inertia of shaft)/(5*Length of Shaft^4)

Circular Frequency given Static Deflection

LaTeX Go Natural Circular Frequency = 2*pi*0.5615/(sqrt(Static Deflection))

Natural Frequency given Static Deflection

LaTeX Go Frequency = 0.5615/(sqrt(Static Deflection))

Moment of Inertia of Shaft given Circular Frequency Formula

LaTeX Go

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 the number of oscillations per unit time of a system vibrating freely in transverse mode without any external force, Load per unit length is the force per unit length applied to a system, affecting its natural frequency of free transverse vibrations, Length of Shaft is the distance from the axis of rotation to the point of maximum vibration amplitude in a transversely vibrating shaft, Young's Modulus is a measure of the stiffness of a solid material and is used to calculate the natural frequency of free transverse vibrations & Acceleration due to Gravity is the rate of change of velocity of an object under the influence of gravitational force, affecting natural frequency of free transverse vibrations.

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 2 other way(s) to calculate the same, which is/are as follows -

Moment of inertia of shaft = (5*Load per unit length*Length of Shaft^4)/(384*Young's Modulus*Static Deflection)
Moment of inertia of shaft = (4*Frequency^2*Load per unit length*Length of Shaft^4)/(pi^2*Young's Modulus*Acceleration due to Gravity)

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