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Moment of Inertia of shaft in terms of natural frequency Solution

STEP 0: Pre-Calculation Summary
Formula Used
moment_inertia_shaft = ((4*frequency^2)*Load per unit length*(Length of Shaft^4))/((pi^2)*Young's Modulus*Acceleration Due To Gravity)
I = ((4*f^2)*w*(l^4))/((pi^2)*E*g)
This formula uses 1 Constants, 5 Variables
Constants Used
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
Variables Used
frequency - Frequency refers to the number of occurrences of a periodic event per time and is measured in cycles/second. (Measured in Cycle per Second)
Load per unit length- Load per unit length is the distributed load which is spread over a surface or line.
Length of Shaft - The Length of Shaft is the distance between two ends of shaft. (Measured in Meter)
Young's Modulus - Young's Modulus which can also be called elastic modulus is a mechanical property of linear elastic solid substances. It describes the relationship between stress (force per unit area) and strain (proportional deformation in an object). (Measured in Gigapascal)
Acceleration Due To Gravity - The Acceleration Due To Gravity is acceleration gained by an object because of gravitational force. (Measured in Meter per Square Second)
STEP 1: Convert Input(s) to Base Unit
frequency: 90 Cycle per Second --> 90 Hertz (Check conversion here)
Load per unit length: 3 --> No Conversion Required
Length of Shaft: 50 Meter --> 50 Meter No Conversion Required
Young's Modulus: 100 Gigapascal --> 100000000000 Pascal (Check conversion here)
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 = ((4*f^2)*w*(l^4))/((pi^2)*E*g) --> ((4*90^2)*3*(50^4))/((pi^2)*100000000000*9.8)
Evaluating ... ...
I = 0.0628087949619594
STEP 3: Convert Result to Output's Unit
0.0628087949619594 Kilogram Meter² --> No Conversion Required
FINAL ANSWER
0.0628087949619594 Kilogram Meter² <-- Moment of inertia of the shaft
(Calculation completed in 00.016 seconds)

10+ Natural Frequency of Free Transverse Vibrations Due to Uniformly Distributed Load Acting Over a Simply Supported Shaft Calculators

Length of the shaft in terms of circular frequency
length_of_shaft = (((pi^4)/(Natural circular frequency^2))*((Young's Modulus*Moment of inertia of the shaft*Acceleration Due To Gravity)/((Load per unit length))))^(1/4) Go
Length of the shaft in terms of natural frequency
length_of_shaft = (((pi^2)/(4*(frequency^2)))*((Young's Modulus*Moment of inertia of the shaft*Acceleration Due To Gravity)/((Load per unit length))))^(1/4) Go
Moment of Inertia of shaft in terms of circular frequency
moment_inertia_shaft = ((Natural circular frequency^2)*Load per unit length*(Length of Shaft^4))/((pi^4)*Young's Modulus*Acceleration Due To Gravity) Go
Moment of Inertia of shaft in terms of natural frequency
moment_inertia_shaft = ((4*frequency^2)*Load per unit length*(Length of Shaft^4))/((pi^2)*Young's Modulus*Acceleration Due To Gravity) Go
Length of the shaft in terms of static deflection
length_of_shaft = ((Static deflection*384*Young's Modulus*Moment of inertia of the shaft)/(5*Load per unit length))^(1/4) Go
Uniformly distributed load unit length in terms of static deflection
load_per_unit_length = ((Static deflection*384*Young's Modulus*Moment of inertia of the shaft)/(5*(Length of Shaft^4))) Go
Static deflection of a simply supported shaft due to uniformly distributed load
static_deflection = (5*Load per unit length*(Length of Shaft^4))/(384*Young's Modulus*Moment of inertia of the shaft) Go
Moment of Inertia of shaft in terms of static deflection if load per unit length is known
moment_inertia_shaft = (5*Load per unit length*(Length of Shaft^4))/(384*Young's Modulus*Static deflection) Go
Circular frequency in terms of static deflection
natural_circular_frequency = 2*pi*(0.5615/(sqrt(Static deflection))) Go
Natural frequency in terms of static deflection
frequency = 0.5615/(sqrt(Static deflection)) Go

Moment of Inertia of shaft in terms of natural frequency Formula

moment_inertia_shaft = ((4*frequency^2)*Load per unit length*(Length of Shaft^4))/((pi^2)*Young's Modulus*Acceleration Due To Gravity)
I = ((4*f^2)*w*(l^4))/((pi^2)*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 in terms of natural frequency?

Moment of Inertia of shaft in terms of natural frequency calculator uses moment_inertia_shaft = ((4*frequency^2)*Load per unit length*(Length of Shaft^4))/((pi^2)*Young's Modulus*Acceleration Due To Gravity) to calculate the Moment of inertia of the shaft, The Moment of Inertia of shaft in terms of natural frequency formula is defined as the quantity expressed by the body resisting angular acceleration which is the sum of the product of the mass of every particle with its square of a distance from the axis of rotation. Moment of inertia of the shaft and is denoted by I symbol.

How to calculate Moment of Inertia of shaft in terms of natural frequency using this online calculator? To use this online calculator for Moment of Inertia of shaft in terms of natural frequency, enter frequency (f), Load per unit length (w), Length of Shaft (l), Young's Modulus (E) and Acceleration Due To Gravity (g) and hit the calculate button. Here is how the Moment of Inertia of shaft in terms of natural frequency calculation can be explained with given input values -> 0.062809 = ((4*90^2)*3*(50^4))/((pi^2)*100000000000*9.8).

FAQ

What is Moment of Inertia of shaft in terms of natural frequency?
The Moment of Inertia of shaft in terms of natural frequency formula is defined as the quantity expressed by the body resisting angular acceleration which is the sum of the product of the mass of every particle with its square of a distance from the axis of rotation and is represented as I = ((4*f^2)*w*(l^4))/((pi^2)*E*g) or moment_inertia_shaft = ((4*frequency^2)*Load per unit length*(Length of Shaft^4))/((pi^2)*Young's Modulus*Acceleration Due To Gravity). Frequency refers to the number of occurrences of a periodic event per time and is measured in cycles/second, Load per unit length is the distributed load which is spread over a surface or line, The Length of Shaft is the distance between two ends of shaft, Young's Modulus which can also be called elastic modulus is a mechanical property of linear elastic solid substances. It describes the relationship between stress (force per unit area) and strain (proportional deformation in an object) and The Acceleration Due To Gravity is acceleration gained by an object because of gravitational force.
How to calculate Moment of Inertia of shaft in terms of natural frequency?
The Moment of Inertia of shaft in terms of natural frequency formula is defined as the quantity expressed by the body resisting angular acceleration which is the sum of the product of the mass of every particle with its square of a distance from the axis of rotation is calculated using moment_inertia_shaft = ((4*frequency^2)*Load per unit length*(Length of Shaft^4))/((pi^2)*Young's Modulus*Acceleration Due To Gravity). To calculate Moment of Inertia of shaft in terms of natural frequency, you need frequency (f), Load per unit length (w), Length of Shaft (l), Young's Modulus (E) and Acceleration Due To Gravity (g). With our tool, you need to enter the respective value for frequency, Load per unit length, Length of Shaft, Young's Modulus and 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 the shaft?
In this formula, Moment of inertia of the shaft uses frequency, Load per unit length, Length of Shaft, Young's Modulus and Acceleration Due To Gravity. We can use 10 other way(s) to calculate the same, which is/are as follows -
  • natural_circular_frequency = 2*pi*(0.5615/(sqrt(Static deflection)))
  • frequency = 0.5615/(sqrt(Static deflection))
  • load_per_unit_length = ((Static deflection*384*Young's Modulus*Moment of inertia of the shaft)/(5*(Length of Shaft^4)))
  • length_of_shaft = ((Static deflection*384*Young's Modulus*Moment of inertia of the shaft)/(5*Load per unit length))^(1/4)
  • moment_inertia_shaft = (5*Load per unit length*(Length of Shaft^4))/(384*Young's Modulus*Static deflection)
  • static_deflection = (5*Load per unit length*(Length of Shaft^4))/(384*Young's Modulus*Moment of inertia of the shaft)
  • moment_inertia_shaft = ((4*frequency^2)*Load per unit length*(Length of Shaft^4))/((pi^2)*Young's Modulus*Acceleration Due To Gravity)
  • moment_inertia_shaft = ((Natural circular frequency^2)*Load per unit length*(Length of Shaft^4))/((pi^4)*Young's Modulus*Acceleration Due To Gravity)
  • length_of_shaft = (((pi^2)/(4*(frequency^2)))*((Young's Modulus*Moment of inertia of the shaft*Acceleration Due To Gravity)/((Load per unit length))))^(1/4)
  • length_of_shaft = (((pi^4)/(Natural circular frequency^2))*((Young's Modulus*Moment of inertia of the shaft*Acceleration Due To Gravity)/((Load per unit length))))^(1/4)
Where is the Moment of Inertia of shaft in terms of natural frequency calculator used?
Among many, Moment of Inertia of shaft in terms of natural frequency calculator is widely used in real life applications like {FormulaUses}. Here are few more real life examples -
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