Moment of Inertia of Pulley's Arm given Minor Axis of Elliptical Section Arm Solution

STEP 0: Pre-Calculation Summary
Formula Used
Area moment of inertia of arms = pi*Minor Axis of Pulley Arm^4/8
I = pi*a^4/8
This formula uses 1 Constants, 2 Variables
Constants Used
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
Variables Used
Area moment of inertia of arms - (Measured in Meter⁴) - Area moment of inertia of arms is the measure of the resistance of the arms of a part its angular acceleration about a given axis without considering its mass.
Minor Axis of Pulley Arm - (Measured in Meter) - Minor Axis of Pulley Arm is the length of the minor or the smallest axis of the elliptical cross-section of a pulley.
STEP 1: Convert Input(s) to Base Unit
Minor Axis of Pulley Arm: 13.66 Millimeter --> 0.01366 Meter (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
I = pi*a^4/8 --> pi*0.01366^4/8
Evaluating ... ...
I = 1.36729644014482E-08
STEP 3: Convert Result to Output's Unit
1.36729644014482E-08 Meter⁴ -->13672.9644014482 Millimeter⁴ (Check conversion here)
FINAL ANSWER
13672.9644014482 13672.96 Millimeter⁴ <-- Area moment of inertia of arms
(Calculation completed in 00.004 seconds)

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Osmania University (OU), Hyderabad
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23 Arms of Cast Iron Pulley Calculators

Minor Axis of Elliptical Cross-Section of Pulley's Arm given Torque and Bending Stress
Go Minor Axis of Pulley Arm = (16*Torque Transmitted by Pulley/(pi*Number of Arms in Pulley*Bending stress in pulley's arm))^(1/3)
Bending Stress in Arm of Belt Driven Pulley given Torque Transmitted by Pulley
Go Bending stress in pulley's arm = 16*Torque Transmitted by Pulley/(pi*Number of Arms in Pulley*Minor Axis of Pulley Arm^3)
Torque Transmitted by Pulley given Bending Stress in Arm
Go Torque Transmitted by Pulley = Bending stress in pulley's arm*(pi*Number of Arms in Pulley*Minor Axis of Pulley Arm^3)/16
Number of Arms of Pulley given Bending Stress in Arm
Go Number of Arms in Pulley = 16*Torque Transmitted by Pulley/(pi*Bending stress in pulley's arm*Minor Axis of Pulley Arm^3)
Tangential Force at End of Each Arm of Pulley given Torque Transmitted by Pulley
Go Tangential Force at End of Each Pulley Arm = Torque Transmitted by Pulley/(Radius of Rim of Pulley*(Number of Arms in Pulley/2))
Radius of Rim of Pulley given Torque Transmitted by Pulley
Go Radius of Rim of Pulley = Torque Transmitted by Pulley/(Tangential Force at End of Each Pulley Arm*(Number of Arms in Pulley/2))
Number of Arms of Pulley given Torque Transmitted by Pulley
Go Number of Arms in Pulley = 2*Torque Transmitted by Pulley/(Tangential Force at End of Each Pulley Arm*Radius of Rim of Pulley)
Torque Transmitted by Pulley
Go Torque Transmitted by Pulley = Tangential Force at End of Each Pulley Arm*Radius of Rim of Pulley*(Number of Arms in Pulley/2)
Bending Moment on Arm of Belt Driven Pulley given Bending Stress in Arm
Go Bending moment in pulley's arm = Area moment of inertia of arms*Bending stress in pulley's arm/Minor Axis of Pulley Arm
Moment of Inertia of Pulley's Arm given Bending Stress in Arm
Go Area moment of inertia of arms = Bending moment in pulley's arm*Minor Axis of Pulley Arm/Bending stress in pulley's arm
Bending Stress in Arm of Belt Driven Pulley
Go Bending stress in pulley's arm = Bending moment in pulley's arm*Minor Axis of Pulley Arm/Area moment of inertia of arms
Major Axis of Elliptical Cross-Section of Pulley's Arm given Moment of Inertia of Arm
Go Major Axis of Pulley Arm = (64*Area moment of inertia of arms/(pi*Minor Axis of Pulley Arm))^(1/3)
Minor Axis of Elliptical Cross-Section of Arm given Moment of Inertia of Arm
Go Minor Axis of Pulley Arm = 64*Area moment of inertia of arms/(pi*Major Axis of Pulley Arm^3)
Moment of Inertia of Pulley's Arm
Go Area moment of inertia of arms = (pi*Minor Axis of Pulley Arm*Major Axis of Pulley Arm^3)/64
Minor Axis of Elliptical Cross-Section of Pulley's Arm given Bending Stress in Arm
Go Minor Axis of Pulley Arm = 1.72*((Bending moment in pulley's arm/(2*Bending stress in pulley's arm))^(1/3))
Tangential Force at End of Each Arm of Pulley given Bending Moment on Arm
Go Tangential Force at End of Each Pulley Arm = Bending moment in pulley's arm/Radius of Rim of Pulley
Radius of Rim of Pulley given Bending Moment Acting on Arm
Go Radius of Rim of Pulley = Bending moment in pulley's arm/Tangential Force at End of Each Pulley Arm
Bending Moment on Arm of Belt Driven Pulley
Go Bending moment in pulley's arm = Tangential Force at End of Each Pulley Arm*Radius of Rim of Pulley
Bending Moment on Arm of Belt Driven Pulley given Torque Transmitted by Pulley
Go Bending moment in pulley's arm = 2*Torque Transmitted by Pulley/Number of Arms in Pulley
Torque Transmitted by Pulley given Bending Moment on Arm
Go Torque Transmitted by Pulley = Bending moment in pulley's arm*Number of Arms in Pulley/2
Number of Arms of Pulley given Bending Moment on Arm
Go Number of Arms in Pulley = 2*Torque Transmitted by Pulley/Bending moment in pulley's arm
Minor Axis of Elliptical Cross-Section of Pulley's Arm given Moment of Inertia of Arm
Go Minor Axis of Pulley Arm = (8*Area moment of inertia of arms/pi)^(1/4)
Moment of Inertia of Pulley's Arm given Minor Axis of Elliptical Section Arm
Go Area moment of inertia of arms = pi*Minor Axis of Pulley Arm^4/8

Moment of Inertia of Pulley's Arm given Minor Axis of Elliptical Section Arm Formula

Area moment of inertia of arms = pi*Minor Axis of Pulley Arm^4/8
I = pi*a^4/8

Define Moment of Inertia?

The moment of inertia, otherwise known as the mass moment of inertia, angular mass, second moment of mass, or most accurately, rotational inertia, of a rigid body, is a quantity that determines the torque needed for a desired angular acceleration about a rotational axis, akin to how mass determines the force needed for the desired acceleration.

How to Calculate Moment of Inertia of Pulley's Arm given Minor Axis of Elliptical Section Arm?

Moment of Inertia of Pulley's Arm given Minor Axis of Elliptical Section Arm calculator uses Area moment of inertia of arms = pi*Minor Axis of Pulley Arm^4/8 to calculate the Area moment of inertia of arms, Moment of Inertia of Pulley's Arm given Minor Axis of Elliptical Section Arm formula is defined as the tendency to resist angular acceleration, which is the sum of the products of the mass of each particle in the body with the square of its distance from the axis of rotation. Area moment of inertia of arms is denoted by I symbol.

How to calculate Moment of Inertia of Pulley's Arm given Minor Axis of Elliptical Section Arm using this online calculator? To use this online calculator for Moment of Inertia of Pulley's Arm given Minor Axis of Elliptical Section Arm, enter Minor Axis of Pulley Arm (a) and hit the calculate button. Here is how the Moment of Inertia of Pulley's Arm given Minor Axis of Elliptical Section Arm calculation can be explained with given input values -> 1.4E+16 = pi*0.01366^4/8.

FAQ

What is Moment of Inertia of Pulley's Arm given Minor Axis of Elliptical Section Arm?
Moment of Inertia of Pulley's Arm given Minor Axis of Elliptical Section Arm formula is defined as the tendency to resist angular acceleration, which is the sum of the products of the mass of each particle in the body with the square of its distance from the axis of rotation and is represented as I = pi*a^4/8 or Area moment of inertia of arms = pi*Minor Axis of Pulley Arm^4/8. Minor Axis of Pulley Arm is the length of the minor or the smallest axis of the elliptical cross-section of a pulley.
How to calculate Moment of Inertia of Pulley's Arm given Minor Axis of Elliptical Section Arm?
Moment of Inertia of Pulley's Arm given Minor Axis of Elliptical Section Arm formula is defined as the tendency to resist angular acceleration, which is the sum of the products of the mass of each particle in the body with the square of its distance from the axis of rotation is calculated using Area moment of inertia of arms = pi*Minor Axis of Pulley Arm^4/8. To calculate Moment of Inertia of Pulley's Arm given Minor Axis of Elliptical Section Arm, you need Minor Axis of Pulley Arm (a). With our tool, you need to enter the respective value for Minor Axis of Pulley Arm 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 Area moment of inertia of arms?
In this formula, Area moment of inertia of arms uses Minor Axis of Pulley Arm. We can use 2 other way(s) to calculate the same, which is/are as follows -
  • Area moment of inertia of arms = (pi*Minor Axis of Pulley Arm*Major Axis of Pulley Arm^3)/64
  • Area moment of inertia of arms = Bending moment in pulley's arm*Minor Axis of Pulley Arm/Bending stress in pulley's arm
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