M.I of Shaft given Natural Frequency for Fixed Shaft and Uniformly Distributed Load Solution

STEP 0: Pre-Calculation Summary
Formula Used
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)
Ishaft = (f^2*w*Lshaft^4)/(3.573^2*E*g)
This formula uses 6 Variables
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 = (f^2*w*Lshaft^4)/(3.573^2*E*g) --> (90^2*3*4.5^4)/(3.573^2*15*9.8)
Evaluating ... ...
Ishaft = 5309.73640399951
STEP 3: Convert Result to Output's Unit
5309.73640399951 Kilogram Square Meter --> No Conversion Required
FINAL ANSWER
5309.73640399951 5309.736 Kilogram Square Meter <-- Moment of inertia of shaft
(Calculation completed in 00.004 seconds)

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17 Natural Frequency of Free Transverse Vibrations of a Shaft Fixed at Both Ends Carrying a Uniformly Distributed Load Calculators

Static Deflection at Distance x from End A given Length of Shaft
Go Static deflection at distance x from end A = (Load per unit length/(24*Young's Modulus*Moment of inertia of shaft))*(Distance of small section of shaft from end A^4+(Length of Shaft*Distance of small section of shaft from end A)^2-2*Length of Shaft*Distance of small section of shaft from end A^3)
Bending Moment at Some Distance from One End
Go Bending Moment = ((Load per unit length*Length of Shaft^2)/12)+((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)
Natural Circular Frequency of Shaft Fixed at Both Ends and Carrying Uniformly Distributed Load
Go Natural Circular Frequency = sqrt((504*Young's Modulus*Moment of inertia of shaft*Acceleration due to Gravity)/(Load per unit length*Length of Shaft^4))
Natural Frequency of Shaft Fixed at Both Ends and Carrying Uniformly Distributed Load
Go Frequency = 3.573*sqrt((Young's Modulus*Moment of inertia of shaft*Acceleration due to Gravity)/(Load per unit length*Length of Shaft^4))
Length of Shaft given Natural Circular Frequency (Shaft Fixed, Uniformly Distributed Load)
Go Length of Shaft = ((504*Young's Modulus*Moment of inertia of shaft*Acceleration due to Gravity)/(Load per unit length*Natural Circular Frequency^2))^(1/4)
Load given Natural Circular Frequency (Shaft Fixed, Uniformly Distributed Load)
Go Load per unit length = ((504*Young's Modulus*Moment of inertia of shaft*Acceleration due to Gravity)/(Length of Shaft^4*Natural Circular Frequency^2))
M.I of Shaft given Natural Circular Frequency (Shaft Fixed, Uniformly Distributed Load)
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)
Length of Shaft given Natural Frequency (Shaft Fixed, Uniformly Distributed Load)
Go Length of Shaft = 3.573^2*((Young's Modulus*Moment of inertia of shaft*Acceleration due to Gravity)/(Load per unit length*Frequency^2))^(1/4)
Load given Natural Frequency for Fixed Shaft and Uniformly Distributed Load
Go Load per unit length = (3.573^2)*((Young's Modulus*Moment of inertia of shaft*Acceleration due to Gravity)/(Length of Shaft^4*Frequency^2))
M.I of Shaft given Natural Frequency for Fixed Shaft and Uniformly Distributed Load
Go 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)
Length of Shaft in given Static Deflection (Shaft Fixed, Uniformly Distributed Load)
Go Length of Shaft = ((Static Deflection*384*Young's Modulus*Moment of inertia of shaft)/(Load per unit length))^(1/4)
Load using Static Deflection (Shaft Fixed, Uniformly Distributed Load)
Go Load per unit length = ((Static Deflection*384*Young's Modulus*Moment of inertia of shaft)/(Length of Shaft^4))
M.I of Shaft given Static Deflection for Fixed Shaft and Uniformly Distributed Load
Go Moment of inertia of shaft = (Load per unit length*Length of Shaft^4)/(384*Young's Modulus*Static Deflection)
Static Deflection of Shaft due to Uniformly Distributed Load given Length of Shaft
Go Static Deflection = (Load per unit length*Length of Shaft^4)/(384*Young's Modulus*Moment of inertia of shaft)
Circular Frequency given Static Deflection (Shaft Fixed, Uniformly Distributed Load)
Go Natural Circular Frequency = (2*pi*0.571)/(sqrt(Static Deflection))
Natural Frequency given Static Deflection (Shaft Fixed, Uniformly Distributed Load)
Go Frequency = 0.571/(sqrt(Static Deflection))
Static Deflection given Natural Frequency (Shaft Fixed, Uniformly Distributed Load)
Go Static Deflection = (0.571/Frequency)^2

M.I of Shaft given Natural Frequency for Fixed Shaft and Uniformly Distributed Load Formula

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)
Ishaft = (f^2*w*Lshaft^4)/(3.573^2*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 Frequency for Fixed Shaft and Uniformly Distributed Load?

M.I of Shaft given Natural Frequency for Fixed Shaft and Uniformly Distributed Load calculator uses 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) to calculate the Moment of inertia of shaft, The M.I of shaft given natural frequency for fixed shaft and uniformly distributed load 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 M.I of Shaft given Natural Frequency for Fixed Shaft and Uniformly Distributed Load using this online calculator? To use this online calculator for M.I of Shaft given Natural Frequency for Fixed Shaft and Uniformly Distributed Load, 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 M.I of Shaft given Natural Frequency for Fixed Shaft and Uniformly Distributed Load calculation can be explained with given input values -> 5309.736 = (90^2*3*4.5^4)/(3.573^2*15*9.8).

FAQ

What is M.I of Shaft given Natural Frequency for Fixed Shaft and Uniformly Distributed Load?
The M.I of shaft given natural frequency for fixed shaft and uniformly distributed load 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 = (f^2*w*Lshaft^4)/(3.573^2*E*g) or 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). 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 M.I of Shaft given Natural Frequency for Fixed Shaft and Uniformly Distributed Load?
The M.I of shaft given natural frequency for fixed shaft and uniformly distributed load 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 = (Frequency^2*Load per unit length*Length of Shaft^4)/(3.573^2*Young's Modulus*Acceleration due to Gravity). To calculate M.I of Shaft given Natural Frequency for Fixed Shaft and Uniformly Distributed Load, 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 = (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)/(504*Young's Modulus*Acceleration due to Gravity)
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