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

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Equivalent Mass of Geared System is the effective mass of a geared system, considering the moment of inertia and kinetic energy of the system. Check FAQs

MOI = I A + \frac{G^{2} \cdot I B}{η}

MOI - Equivalent Mass of Geared System?I_A - Mass Moment of Inertia of Mass Attached to Shaft A?G - Gear Ratio?I_B - Mass Moment of Inertia of Mass Attached to Shaft B?η - Gear Efficiency?

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

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Here is how the Equivalent Mass Moment of Inertia of Geared System with Shaft A and Shaft B equation looks like with Values.

Here is how the Equivalent Mass Moment of Inertia of Geared System with Shaft A and Shaft B equation looks like with Units.

Here is how the Equivalent Mass Moment of Inertia of Geared System with Shaft A and Shaft B equation looks like.

413.122 = 18 + \frac{3^{2} \cdot 36}{0.82}

413.122kg·m² = 18kg·m² + \frac{3^{2} \cdot 36kg·m²}{0.82}

413.122 = 18 + \frac{3^{2} \cdot 36}{0.82}

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

Follow our step by step solution on how to calculate Equivalent Mass Moment of Inertia of Geared System with Shaft A and Shaft B?

FIRST Step Consider the formula

MOI = I A + \frac{G^{2} \cdot I B}{η}

Next Step Substitute values of Variables

∴

MOI = 18kg·m² + \frac{3^{2} \cdot 36kg·m²}{0.82}

Next Step Prepare to Evaluate

∴

MOI = 18 + \frac{3^{2} \cdot 36}{0.82}

Next Step Evaluate

∴

MOI = 413.121951219512kg·m²

LAST Step Rounding Answer

∴

MOI = 413.122kg·m²

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

Variables

Equivalent Mass of Geared System

Equivalent Mass of Geared System is the effective mass of a geared system, considering the moment of inertia and kinetic energy of the system.

Symbol: MOI

Measurement: Moment of InertiaUnit: kg·m²

Note: Value can be positive or negative.

Formulas to find Equivalent Mass of Geared System

Mass Moment of Inertia of Mass Attached to Shaft A

Mass Moment of Inertia of Mass Attached to Shaft A is a measure of an object's resistance to changes in its rotation.

Symbol: I_A

Measurement: Moment of InertiaUnit: kg·m²

Note: Value should be greater than 0.

Formulas to find Mass Moment of Inertia of Mass Attached to Shaft A

Gear Ratio

Gear Ratio is the ratio of the angular velocity of the output shaft to the angular velocity of the input shaft in a mechanical system.

Symbol: G

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Gear Ratio

Mass Moment of Inertia of Mass Attached to Shaft B

Mass Moment of Inertia of Mass Attached to Shaft B is a measure of an object's resistance to changes in its rotational motion around a specific axis.

Symbol: I_B

Measurement: Moment of InertiaUnit: kg·m²

Note: Value should be greater than 0.

Formulas to find Mass Moment of Inertia of Mass Attached to Shaft B

Gear Efficiency

Gear Efficiency is the ratio of output power to input power of a gear system, indicating the system's ability to transmit power efficiently.

Symbol: η

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Gear Efficiency

Other formulas in Kinetics category

Go Angular Acceleration of Shaft B given Gear Ratio and Angular Acceleration of Shaft A

α B = G \cdot α A

Go Angular Velocity given Speed in RPM

ω = \frac{2 \cdot π \cdot N A}{60}

Go Centripetal Force or Centrifugal Force for given Angular Velocity and Radius of Curvature

Fc = Mass flight path \cdot ω^{2} \cdot R c

Go Coefficient of Restitution

e = \frac{v 1 - v 2}{u 2 - u 1}

How to Evaluate 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 evaluator uses Equivalent Mass 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 evaluate the Equivalent Mass of Geared System, Equivalent Mass Moment of Inertia of Geared System with Shaft A and Shaft B formula is defined as a measure of the rotational inertia of a geared system, considering the moments of inertia of Shaft A and Shaft B, and the gear ratio, which affects the overall rotational motion of the system. Equivalent Mass of Geared System is denoted by MOI symbol.

How to evaluate Equivalent Mass Moment of Inertia of Geared System with Shaft A and Shaft B using this online evaluator? To use this online evaluator 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 (I_A), Gear Ratio (G), Mass Moment of Inertia of Mass Attached to Shaft B (I_B) & Gear Efficiency (η) and hit the calculate button.

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

What is the formula to find Equivalent Mass Moment of Inertia of Geared System with Shaft A and Shaft B?

The formula of Equivalent Mass Moment of Inertia of Geared System with Shaft A and Shaft B is expressed as Equivalent Mass 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. Here is an example- 413.122 = 18+(3^2*36)/0.82.

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

With Mass Moment of Inertia of Mass Attached to Shaft A (I_A), Gear Ratio (G), Mass Moment of Inertia of Mass Attached to Shaft B (I_B) & Gear Efficiency (η) we can find Equivalent Mass Moment of Inertia of Geared System with Shaft A and Shaft B using the formula - Equivalent Mass 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.

Can the Equivalent Mass Moment of Inertia of Geared System with Shaft A and Shaft B be negative?

Yes, the Equivalent Mass Moment of Inertia of Geared System with Shaft A and Shaft B, measured in Moment of Inertia can be negative.

Which unit is used to measure 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 is usually measured using the Kilogram Square Meter[kg·m²] for Moment of Inertia. Kilogram Square Centimeter[kg·m²], Kilogram Square Millimeter[kg·m²], Gram Square Centimeter[kg·m²] are the few other units in which Equivalent Mass Moment of Inertia of Geared System with Shaft A and Shaft B can be measured.

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

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

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

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

Other formulas in Kinetics category

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

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

Variable Name