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Moment of Inertia of the arms of the Pulley Solution

STEP 0: Pre-Calculation Summary
Formula Used
moment_of_inertia = pi*Minor axis*Major axis^3/64
I = pi*b*a^3/64
This formula uses 1 Constants, 2 Variables
Constants Used
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
Variables Used
Minor axis - Minor axis is the line segment that is perpendicular to the major axis and intersects at the center of the ellipse. (Measured in Centimeter)
Major axis - Major axis is the line segment that crosses both the focal points of the ellipse. (Measured in Centimeter)
STEP 1: Convert Input(s) to Base Unit
Minor axis: 5 Centimeter --> 0.05 Meter (Check conversion here)
Major axis: 10 Centimeter --> 0.1 Meter (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
I = pi*b*a^3/64 --> pi*0.05*0.1^3/64
Evaluating ... ...
I = 2.45436926061703E-06
STEP 3: Convert Result to Output's Unit
2.45436926061703E-06 Kilogram Meter² --> No Conversion Required
FINAL ANSWER
2.45436926061703E-06 Kilogram Meter² <-- Moment of Inertia
(Calculation completed in 00.014 seconds)

10+ Arms of Cast Iron Pulley Calculators

Radius of Rim When Torque Transmitted by the Pulley is Given
radius_of_rim = Torque Transmitted by the Pulley/(Tangential Force at the end of Each Arm*(Number of arms/2)) Go
Number of Arms of the Pulley When Torque Transmitted by the Pulley is Given
number_of_arms = 2*Torque Transmitted by the Pulley/(Tangential Force at the end of Each Arm*Radius of Rim) Go
Torque Transmitted by the Pulley
torque_transmitted_by_the_pulley = Tangential Force at the end of Each Arm*Radius of Rim*(Number of arms/2) Go
Tangential Force at the End of Each Arm When Torque Transmitted by the Pulley is Given
tangential_force_at_end_of_each_arm = Torque Transmitted by the Pulley/(Radius of Rim*(Number of arms/2)) Go
Radius of Rim When Bending Moment Acting on the Arm is Given
radius_of_rim = Bending moment/Tangential Force at the end of Each Arm Go
Bending Moment Acting on the arm
bending_moment = Tangential Force at the end of Each Arm*Radius of Rim Go
Tangential Force at the End of Each Arm When Bending Moment acting on the Arm is Given
tangential_force_at_end_of_each_arm = Bending moment/Radius of Rim Go
Torque Transmitted by the Pulley When Bending Moment acting on the Arm is Given
torque_transmitted_by_the_pulley = Bending moment*Number of arms/2 Go
Bending Moment acting on the Arm in terms of Torque Transmitted by the Pulley
bending_moment = 2*Torque Transmitted by the Pulley/Number of arms Go
Number of Arms When Bending Moment acting on the Arm is Given
number_of_arms = 2*Torque Transmitted by the Pulley/Bending moment Go

Moment of Inertia of the arms of the Pulley Formula

moment_of_inertia = pi*Minor axis*Major axis^3/64
I = pi*b*a^3/64

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 a desired acceleration.

How to Calculate Moment of Inertia of the arms of the Pulley?

Moment of Inertia of the arms of the Pulley calculator uses moment_of_inertia = pi*Minor axis*Major axis^3/64 to calculate the Moment of Inertia, The Moment of Inertia of the arms of the Pulley 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. Moment of Inertia and is denoted by I symbol.

How to calculate Moment of Inertia of the arms of the Pulley using this online calculator? To use this online calculator for Moment of Inertia of the arms of the Pulley, enter Minor axis (b) and Major axis (a) and hit the calculate button. Here is how the Moment of Inertia of the arms of the Pulley calculation can be explained with given input values -> 2.454E-6 = pi*0.05*0.1^3/64.

FAQ

What is Moment of Inertia of the arms of the Pulley?
The Moment of Inertia of the arms of the Pulley 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*b*a^3/64 or moment_of_inertia = pi*Minor axis*Major axis^3/64. Minor axis is the line segment that is perpendicular to the major axis and intersects at the center of the ellipse and Major axis is the line segment that crosses both the focal points of the ellipse.
How to calculate Moment of Inertia of the arms of the Pulley?
The Moment of Inertia of the arms of the Pulley 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 moment_of_inertia = pi*Minor axis*Major axis^3/64. To calculate Moment of Inertia of the arms of the Pulley, you need Minor axis (b) and Major axis (a). With our tool, you need to enter the respective value for Minor axis and Major axis 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?
In this formula, Moment of Inertia uses Minor axis and Major axis. We can use 10 other way(s) to calculate the same, which is/are as follows -
  • torque_transmitted_by_the_pulley = Tangential Force at the end of Each Arm*Radius of Rim*(Number of arms/2)
  • tangential_force_at_end_of_each_arm = Torque Transmitted by the Pulley/(Radius of Rim*(Number of arms/2))
  • radius_of_rim = Torque Transmitted by the Pulley/(Tangential Force at the end of Each Arm*(Number of arms/2))
  • number_of_arms = 2*Torque Transmitted by the Pulley/(Tangential Force at the end of Each Arm*Radius of Rim)
  • bending_moment = Tangential Force at the end of Each Arm*Radius of Rim
  • tangential_force_at_end_of_each_arm = Bending moment/Radius of Rim
  • radius_of_rim = Bending moment/Tangential Force at the end of Each Arm
  • bending_moment = 2*Torque Transmitted by the Pulley/Number of arms
  • number_of_arms = 2*Torque Transmitted by the Pulley/Bending moment
  • torque_transmitted_by_the_pulley = Bending moment*Number of arms/2
Where is the Moment of Inertia of the arms of the Pulley calculator used?
Among many, Moment of Inertia of the arms of the Pulley calculator is widely used in real life applications like {FormulaUses}. Here are few more real life examples -
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