Equivalent Mass Moment of Inertia of Geared System with Shaft A and Shaft B Solution

STEP 0: Pre-Calculation Summary
Formula Used
Equivalent Mass MOI of Geared System = Mass Moment of Inertia of Mass Attached to Shaft A+(Gear Ratio^2*Mass Moment of Inertia of Mass Attached to Shaft B)/Gear Efficiency
I = IA+(G^2*IB)/η
This formula uses 5 Variables
Variables Used
Equivalent Mass MOI of Geared System - (Measured in Kilogram Square Meter) - Equivalent Mass MOI of Geared System with Shaft A and B, is a quantity that determines the torque needed for a desired angular acceleration about a rotational axis.
Mass Moment of Inertia of Mass Attached to Shaft A - (Measured in Kilogram Square Meter) - Mass Moment of Inertia of mass attached to shaft A is a quantity expressing a body's tendency to resist angular acceleration.
Gear Ratio - The Gear Ratio is the ratio of output gear speed to the input gear speed or the ratio of number of teeth on gear to that on the pinion.
Mass Moment of Inertia of Mass Attached to Shaft B - (Measured in Kilogram Square Meter) - Mass Moment of Inertia of mass attached to shaft B is a quantity expressing a body's tendency to resist angular acceleration.
Gear Efficiency - Gear Efficiency is simply the ratio of output shaft power to the Input shaft power.
STEP 1: Convert Input(s) to Base Unit
Mass Moment of Inertia of Mass Attached to Shaft A: 18 Kilogram Square Meter --> 18 Kilogram Square Meter No Conversion Required
Gear Ratio: 3 --> No Conversion Required
Mass Moment of Inertia of Mass Attached to Shaft B: 36 Kilogram Square Meter --> 36 Kilogram Square Meter No Conversion Required
Gear Efficiency: 0.82 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
I = IA+(G^2*IB)/η --> 18+(3^2*36)/0.82
Evaluating ... ...
I = 413.121951219512
STEP 3: Convert Result to Output's Unit
413.121951219512 Kilogram Square Meter --> No Conversion Required
FINAL ANSWER
413.121951219512 413.122 Kilogram Square Meter <-- Equivalent Mass MOI of Geared System
(Calculation completed in 00.004 seconds)

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17 Kinetics Calculators

Loss of Kinetic Energy during Perfectly Inelastic Collision
Go Loss of K.E During Perfectly Inelastic Collision = (Mass of Body A*Mass of Body B*(Initial Velocity of Body A Before the Collision-Initial Velocity of Body B Before the Collision)^2)/(2*(Mass of Body A+Mass of Body B))
Final Velocity of Bodies A and B after Inelastic Collision
Go Final Speed of A and B After Inelastic Collision = (Mass of Body A*Initial Velocity of Body A Before the Collision+Mass of Body B*Initial Velocity of Body B Before the Collision)/(Mass of Body A+Mass of Body B)
Coefficient of Restitution
Go Coefficient of Restitution = (Final Velocity of Body A After Elastic Collision-Final Velocity of Body B After Elastic Collision)/(Initial Velocity of Body B Before the Collision-Initial Velocity of Body A Before the Collision)
Equivalent Mass Moment of Inertia of Geared System with Shaft A and Shaft B
Go Equivalent Mass MOI of Geared System = Mass Moment of Inertia of Mass Attached to Shaft A+(Gear Ratio^2*Mass Moment of Inertia of Mass Attached to Shaft B)/Gear Efficiency
Kinetic Energy of System after Inelastic Collision
Go Kinetic Energy of System After Inelastic Collision = ((Mass of Body A+Mass of Body B)*Final Speed of A and B After Inelastic Collision^2)/2
Impulsive Force
Go Impulsive Force = (Mass*(Final Velocity-Initial Velocity))/Time Taken to Travel
Loss of Kinetic Energy during Imperfect Elastic Impact
Go Loss of Kinetic Energy During an Elastic Collision = Loss of K.E During Perfectly Inelastic Collision*(1-Coefficient of Restitution^2)
Speed of Guide Pulley
Go Speed of Guide Pulley = Speed of Drum Pulley*Diameter of Drum Pulley/Diameter of Guide Pulley
Centripetal Force or Centrifugal Force for given Angular Velocity and Radius of Curvature
Go Centripetal Force = Mass*Angular Velocity^2*Radius of Curvature
Total Kinetic Energy of Geared System
Go Kinetic Energy = (Equivalent Mass MOI of Geared System*Angular Acceleration of Shaft A^2)/2
Overall Efficiency from Shaft A to X
Go Overall Efficiency from Shaft A to X = Gear Efficiency^Total no. of Gear Pairs
Angular Acceleration of Shaft B given Gear Ratio and Angular Acceleration of Shaft A
Go Angular Acceleration of Shaft B = Gear Ratio*Angular Acceleration of Shaft A
Gear Ratio when Two Shafts A and B are Geared Together
Go Gear Ratio = Speed of Shaft B in RPM/Speed of Shaft A in RPM
Angular Velocity given Speed in RPM
Go Angular Velocity = (2*pi*Speed of Shaft A in RPM)/60
Efficiency of Machine
Go Gear Efficiency = Output Power/Input Power
Power Loss
Go Power Loss = Input Power-Output Power
Impulse
Go Impulse = Force*Time Taken to Travel

Equivalent Mass Moment of Inertia of Geared System with Shaft A and Shaft B Formula

Equivalent Mass MOI of Geared System = Mass Moment of Inertia of Mass Attached to Shaft A+(Gear Ratio^2*Mass Moment of Inertia of Mass Attached to Shaft B)/Gear Efficiency
I = IA+(G^2*IB)/η

What is the difference between mass and moment of inertia?

The mass of a body usually refers to its inertial mass. The moment of inertia is dependent on the mass of a body. The moment of inertia depends on the axis of rotation and the structure of the body. Inertial mass is the same for a particular body no matter what.

How to Calculate Equivalent Mass Moment of Inertia of Geared System with Shaft A and Shaft B?

Equivalent Mass Moment of Inertia of Geared System with Shaft A and Shaft B calculator uses Equivalent Mass MOI of Geared System = Mass Moment of Inertia of Mass Attached to Shaft A+(Gear Ratio^2*Mass Moment of Inertia of Mass Attached to Shaft B)/Gear Efficiency to calculate the Equivalent Mass MOI of Geared System, The equivalent mass moment of inertia of geared system with shaft A and shaft B is a quantity that determines the torque needed for a desired angular acceleration about a rotational axis; similar to how mass determines the force needed for the desired acceleration. Equivalent Mass MOI of Geared System is denoted by I symbol.

How to calculate Equivalent Mass Moment of Inertia of Geared System with Shaft A and Shaft B using this online calculator? To use this online calculator for Equivalent Mass Moment of Inertia of Geared System with Shaft A and Shaft B, enter Mass Moment of Inertia of Mass Attached to Shaft A (IA), Gear Ratio (G), Mass Moment of Inertia of Mass Attached to Shaft B (IB) & Gear Efficiency (η) and hit the calculate button. Here is how the Equivalent Mass Moment of Inertia of Geared System with Shaft A and Shaft B calculation can be explained with given input values -> 413.122 = 18+(3^2*36)/0.82.

FAQ

What is Equivalent Mass Moment of Inertia of Geared System with Shaft A and Shaft B?
The equivalent mass moment of inertia of geared system with shaft A and shaft B is a quantity that determines the torque needed for a desired angular acceleration about a rotational axis; similar to how mass determines the force needed for the desired acceleration and is represented as I = IA+(G^2*IB)/η or Equivalent Mass MOI of Geared System = Mass Moment of Inertia of Mass Attached to Shaft A+(Gear Ratio^2*Mass Moment of Inertia of Mass Attached to Shaft B)/Gear Efficiency. Mass Moment of Inertia of mass attached to shaft A is a quantity expressing a body's tendency to resist angular acceleration, The Gear Ratio is the ratio of output gear speed to the input gear speed or the ratio of number of teeth on gear to that on the pinion, Mass Moment of Inertia of mass attached to shaft B is a quantity expressing a body's tendency to resist angular acceleration & Gear Efficiency is simply the ratio of output shaft power to the Input shaft power.
How to calculate Equivalent Mass Moment of Inertia of Geared System with Shaft A and Shaft B?
The equivalent mass moment of inertia of geared system with shaft A and shaft B is a quantity that determines the torque needed for a desired angular acceleration about a rotational axis; similar to how mass determines the force needed for the desired acceleration is calculated using Equivalent Mass MOI of Geared System = Mass Moment of Inertia of Mass Attached to Shaft A+(Gear Ratio^2*Mass Moment of Inertia of Mass Attached to Shaft B)/Gear Efficiency. To calculate Equivalent Mass Moment of Inertia of Geared System with Shaft A and Shaft B, you need Mass Moment of Inertia of Mass Attached to Shaft A (IA), Gear Ratio (G), Mass Moment of Inertia of Mass Attached to Shaft B (IB) & Gear Efficiency (η). With our tool, you need to enter the respective value for Mass Moment of Inertia of Mass Attached to Shaft A, Gear Ratio, Mass Moment of Inertia of Mass Attached to Shaft B & Gear Efficiency and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
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