Moment of Inertia of Shaft given Natural Frequency Solution

STEP 0: Pre-Calculation Summary
Formula Used
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)
Ishaft = (4*f^2*w*Lshaft^4)/(pi^2*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.
Frequency - (Measured in Hertz) - Frequency refers to the number of occurrences of a periodic event per time and is measured in cycles/second.
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
Frequency: 90 Hertz --> 90 Hertz No Conversion Required
Load per unit length: 3 --> No Conversion Required
Length of Shaft: 4500 Millimeter --> 4.5 Meter (Check conversion here)
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
Ishaft = (4*f^2*w*Lshaft^4)/(pi^2*E*g) --> (4*90^2*3*4.5^4)/(pi^2*15*9.8)
Evaluating ... ...
Ishaft = 27472.566916361
STEP 3: Convert Result to Output's Unit
27472.566916361 Kilogram Square Meter --> No Conversion Required
FINAL ANSWER
27472.566916361 27472.57 Kilogram Square Meter <-- Moment of inertia of shaft
(Calculation completed in 00.004 seconds)

Credits

Created by Anshika Arya
National Institute Of Technology (NIT), Hamirpur
Anshika Arya has created this Calculator and 2000+ more calculators!
Verified by Dipto Mandal
Indian Institute of Information Technology (IIIT), Guwahati
Dipto Mandal has verified this Calculator and 400+ more calculators!

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

Static Deflection at Distance x from End A
Go Static deflection at distance x from end A = (Load per unit length*(Distance of small section of shaft from end A^4-2*Length of Shaft*Distance of small section of shaft from end A+Length of Shaft^3*Distance of small section of shaft from end A))/(24*Young's Modulus*Moment of inertia of shaft)
Natural Frequency due to Uniformly Distributed Load
Go Frequency = pi/2*sqrt((Young's Modulus*Moment of inertia of shaft*Acceleration due to Gravity)/(Load per unit length*Length of Shaft^4))
Circular Frequency due to Uniformly Distributed Load
Go Natural Circular Frequency = pi^2*sqrt((Young's Modulus*Moment of inertia of shaft*Acceleration due to Gravity)/(Load per unit length*Length of Shaft^4))
Maximum Bending Moment at Distance x from End A
Go Bending Moment = (Load per unit length*Distance of small section of shaft from end A^2)/2-(Load per unit length*Length of Shaft*Distance of small section of shaft from end A)/2
Length of Shaft given Circular Frequency
Go Length of Shaft = ((pi^4)/(Natural Circular Frequency^2)*(Young's Modulus*Moment of inertia of shaft*Acceleration due to Gravity)/(Load per unit length))^(1/4)
Uniformly Distributed Load Unit Length given Circular Frequency
Go Load per unit length = (pi^4)/(Natural Circular Frequency^2)*(Young's Modulus*Moment of inertia of shaft*Acceleration due to Gravity)/(Length of Shaft^4)
Moment of Inertia of Shaft given Circular Frequency
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)
Length of Shaft given Natural Frequency
Go Length of Shaft = ((pi^2)/(4*Frequency^2)*(Young's Modulus*Moment of inertia of shaft*Acceleration due to Gravity)/(Load per unit length))^(1/4)
Uniformly Distributed Load Unit Length given Natural Frequency
Go Load per unit length = (pi^2)/(4*Frequency^2)*(Young's Modulus*Moment of inertia of shaft*Acceleration due to Gravity)/(Length of Shaft^4)
Moment of Inertia of Shaft given Natural Frequency
Go 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)
Length of Shaft given Static Deflection
Go Length of Shaft = ((Static Deflection*384*Young's Modulus*Moment of inertia of shaft)/(5*Load per unit length))^(1/4)
Moment of Inertia of Shaft given Static Deflection given Load per Unit Length
Go Moment of inertia of shaft = (5*Load per unit length*Length of Shaft^4)/(384*Young's Modulus*Static Deflection)
Static Deflection of Simply Supported Shaft due to Uniformly Distributed Load
Go Static Deflection = (5*Load per unit length*Length of Shaft^4)/(384*Young's Modulus*Moment of inertia of shaft)
Uniformly Distributed Load Unit Length given Static Deflection
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
Go Natural Circular Frequency = 2*pi*0.5615/(sqrt(Static Deflection))
Natural Frequency given Static Deflection
Go Frequency = 0.5615/(sqrt(Static Deflection))
Static Deflection using Natural Frequency
Go Static Deflection = (0.5615/Frequency)^2

Moment of Inertia of Shaft given Natural Frequency Formula

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)
Ishaft = (4*f^2*w*Lshaft^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 given Natural Frequency?

Moment of Inertia of Shaft given Natural Frequency calculator uses 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) to calculate the Moment of inertia of shaft, The Moment of Inertia of Shaft given 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 shaft is denoted by Ishaft symbol.

How to calculate Moment of Inertia of Shaft given Natural Frequency using this online calculator? To use this online calculator for Moment of Inertia of Shaft given Natural Frequency, enter Frequency (f), Load per unit length (w), Length of Shaft (Lshaft), Young's Modulus (E) & Acceleration due to Gravity (g) and hit the calculate button. Here is how the Moment of Inertia of Shaft given Natural Frequency calculation can be explained with given input values -> 27472.57 = (4*90^2*3*4.5^4)/(pi^2*15*9.8).

FAQ

What is Moment of Inertia of Shaft given Natural Frequency?
The Moment of Inertia of Shaft given 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 Ishaft = (4*f^2*w*Lshaft^4)/(pi^2*E*g) or 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). 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, 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 Natural Frequency?
The Moment of Inertia of Shaft given 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 of inertia of 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 given Natural Frequency, you need Frequency (f), Load per unit length (w), Length of Shaft (Lshaft), Young's Modulus (E) & 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 & 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 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 = (Natural Circular Frequency^2*Load per unit length*(Length of Shaft^4))/(pi^4*Young's Modulus*Acceleration due to Gravity)
Let Others Know
Facebook
Twitter
Reddit
LinkedIn
Email
WhatsApp
Copied!