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M.I of Shaft given Natural Circular Frequency (Shaft Fixed, Uniformly Distributed Load) Calculator

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

✖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.ⓘ M.I of Shaft given Natural Circular Frequency (Shaft Fixed, Uniformly Distributed Load) [I_shaft]

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M.I of Shaft given Natural Circular Frequency (Shaft Fixed, Uniformly Distributed Load) 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)/(504*Young's Modulus*Acceleration due to Gravity)
I_shaft = (ω_n^2*w*L_shaft^4)/(504*E*g)
This formula uses 6 Variables

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)/(504*E*g) --> (13.1^2*3*3.5^4)/(504*15*9.8)

Evaluating ... ...

I_shaft = 1.04276909722222

STEP 3: Convert Result to Output's Unit

1.04276909722222 Kilogram Square Meter --> No Conversion Required

FINAL ANSWER

1.04276909722222 ≈ 1.042769 Kilogram Square Meter <-- Moment of inertia of shaft

(Calculation completed in 00.020 seconds)

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Home » Physics » Theory of Machine » Vibrations » Longitudinal and Transverse Vibrations » Natural Frequency of Free Transverse Vibrations » Mechanical » Shaft Fixed at Both Ends Carrying a Uniformly Distributed Load » M.I of Shaft given Natural Circular Frequency (Shaft Fixed, Uniformly Distributed Load)

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National Institute Of Technology (NIT), Hamirpur

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< Shaft Fixed at Both Ends Carrying a Uniformly Distributed Load Calculators

M.I of Shaft given Static Deflection for Fixed Shaft and Uniformly Distributed Load

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

Circular Frequency given Static Deflection (Shaft Fixed, Uniformly Distributed Load)

LaTeX Go Natural Circular Frequency = (2*pi*0.571)/(sqrt(Static Deflection))

Natural Frequency given Static Deflection (Shaft Fixed, Uniformly Distributed Load)

LaTeX Go Frequency = 0.571/(sqrt(Static Deflection))

Static Deflection given Natural Frequency (Shaft Fixed, Uniformly Distributed Load)

LaTeX Go Static Deflection = (0.571/Frequency)^2

M.I of Shaft given Natural Circular Frequency (Shaft Fixed, Uniformly Distributed Load) Formula

LaTeX Go

Moment of inertia of shaft = (Natural Circular Frequency^2*Load per unit length*Length of Shaft^4)/(504*Young's Modulus*Acceleration due to Gravity)
I_shaft = (ω_n^2*w*L_shaft^4)/(504*E*g)

What is a Transverse Wave definition?

Transverse wave, motion in which all points on a wave oscillate along paths at right angles to the direction of the wave's advance. Surface ripples on water, seismic S (secondary) waves, and electromagnetic (e.g., radio and light) waves are examples of transverse waves.

How to Calculate M.I of Shaft given Natural Circular Frequency (Shaft Fixed, Uniformly Distributed Load)?

M.I of Shaft given Natural Circular Frequency (Shaft Fixed, Uniformly Distributed Load) calculator uses Moment of inertia of shaft = (Natural Circular Frequency^2*Load per unit length*Length of Shaft^4)/(504*Young's Modulus*Acceleration due to Gravity) to calculate the Moment of inertia of shaft, M.I of Shaft given Natural Circular Frequency (Shaft Fixed, Uniformly Distributed Load) formula is defined as the moment of inertia of a shaft under uniformly distributed load, which is a critical parameter in determining the natural frequency of free transverse vibrations in a shaft. Moment of inertia of shaft is denoted by I_shaft symbol.

How to calculate M.I of Shaft given Natural Circular Frequency (Shaft Fixed, Uniformly Distributed Load) using this online calculator? To use this online calculator for M.I of Shaft given Natural Circular Frequency (Shaft Fixed, Uniformly Distributed Load), 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 M.I of Shaft given Natural Circular Frequency (Shaft Fixed, Uniformly Distributed Load) calculation can be explained with given input values -> 1.042769 = (13.1^2*3*3.5^4)/(504*15*9.8).

FAQ

What is M.I of Shaft given Natural Circular Frequency (Shaft Fixed, Uniformly Distributed Load)?

M.I of Shaft given Natural Circular Frequency (Shaft Fixed, Uniformly Distributed Load) formula is defined as the moment of inertia of a shaft under uniformly distributed load, which is a critical parameter in determining the natural frequency of free transverse vibrations in a shaft and is represented as I_shaft = (ω_n^2*w*L_shaft^4)/(504*E*g) or Moment of inertia of shaft = (Natural Circular Frequency^2*Load per unit length*Length of Shaft^4)/(504*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 M.I of Shaft given Natural Circular Frequency (Shaft Fixed, Uniformly Distributed Load)?

M.I of Shaft given Natural Circular Frequency (Shaft Fixed, Uniformly Distributed Load) formula is defined as the moment of inertia of a shaft under uniformly distributed load, which is a critical parameter in determining the natural frequency of free transverse vibrations in a shaft is calculated using Moment of inertia of shaft = (Natural Circular Frequency^2*Load per unit length*Length of Shaft^4)/(504*Young's Modulus*Acceleration due to Gravity). To calculate M.I of Shaft given Natural Circular Frequency (Shaft Fixed, Uniformly Distributed Load), 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 = (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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