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Polar Moment of Inertia of Shaft for Torsion Dynamometer Formula

GoPolar Moment of Inertia of Shaft for Hollow Shaft for Torsion Dynamometer Formula

GoPolar Moment of Inertia of Shaft for Solid Shaft for Torsion Dynamometer Formula

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Polar Moment of Inertia of Shaft is a measure of an object's resistance to changes in its rotation, important in dynamometer applications. Check FAQs

J = \frac{T \cdot L shaft}{G \cdot θ}

J - Polar Moment of Inertia of Shaft?T - Total Torque?L_shaft - Shaft Length?G - Modulus of Rigidity?θ - Angle of Twist?

Polar Moment of Inertia of Shaft for Torsion Dynamometer Example

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Here is how the Polar Moment of Inertia of Shaft for Torsion Dynamometer equation looks like with Values.

Here is how the Polar Moment of Inertia of Shaft for Torsion Dynamometer equation looks like with Units.

Here is how the Polar Moment of Inertia of Shaft for Torsion Dynamometer equation looks like.

0.09 = \frac{13 \cdot 0.42}{40 \cdot 1.517}

0.09m⁴ = \frac{13N*m \cdot 0.42m}{40N/m² \cdot 1.517rad}

0.09 = \frac{13 \cdot 0.42}{40 \cdot 1.517}

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Polar Moment of Inertia of Shaft for Torsion Dynamometer Solution

Follow our step by step solution on how to calculate Polar Moment of Inertia of Shaft for Torsion Dynamometer?

FIRST Step Consider the formula

J = \frac{T \cdot L shaft}{G \cdot θ}

Next Step Substitute values of Variables

∴

J = \frac{13N*m \cdot 0.42m}{40N/m² \cdot 1.517rad}

Next Step Convert Units

∴

J = \frac{13N*m \cdot 0.42m}{40Pa \cdot 1.517rad}

Next Step Prepare to Evaluate

∴

J = \frac{13 \cdot 0.42}{40 \cdot 1.517}

Next Step Evaluate

∴

J = 0.0899802241265656m⁴

LAST Step Rounding Answer

∴

J = 0.09m⁴

Polar Moment of Inertia of Shaft for Torsion Dynamometer Formula Elements

Variables

Polar Moment of Inertia of Shaft

Polar Moment of Inertia of Shaft is a measure of an object's resistance to changes in its rotation, important in dynamometer applications.

Symbol: J

Measurement: Second Moment of AreaUnit: m⁴

Note: Value should be greater than 0.

Formulas to find Polar Moment of Inertia of Shaft

Total Torque

Total Torque is the rotational force that causes an object to rotate, measured by a dynamometer, typically in units of newton-meters or foot-pounds.

Symbol: T

Measurement: TorqueUnit: N*m

Note: Value can be positive or negative.

Formulas to find Total Torque

Shaft Length

Shaft Length is the distance from the dynamometer's rotating shaft to the point of measurement, typically used to calculate torque and power output.

Symbol: L_shaft

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Shaft Length

Modulus of Rigidity

Modulus of Rigidity is the measure of the stiffness of a material, determining the amount of stress required to produce a unit deformation.

Symbol: G

Measurement: PressureUnit: N/m²

Note: Value should be greater than 0.

Formulas to find Modulus of Rigidity

Angle of Twist

Angle of Twist is the rotational deformation of a shaft measured by a dynamometer, which is used to calculate the torque or rotational force.

Symbol: θ

Measurement: AngleUnit: rad

Note: Value should be greater than 0.

Formulas to find Angle of Twist

Other Formulas to find Polar Moment of Inertia of Shaft

Go Polar Moment of Inertia of Shaft for Hollow Shaft for Torsion Dynamometer

J = \frac{π}{32} \cdot ({d o}^{4} - {d i}^{4})

Go Polar Moment of Inertia of Shaft for Solid Shaft for Torsion Dynamometer

J = \frac{π}{32} \cdot {D shaft}^{4}

Other formulas in Dynamometer category

Go Constant for Particular Shaft for Torsion Dynamometer

k = \frac{G \cdot J}{L shaft}

Go Distance Moved in One Revolution by Rope Brake Dynamometer

d = π \cdot (D wheel + d rope)

Go Load on Brake for Rope Brake Dynamometer

W = W dead - S

Go Tangential Effort for Epicyclic-Train Dynamometer

P t = \frac{W end \cdot L horizontal}{2 \cdot a gear}

How to Evaluate Polar Moment of Inertia of Shaft for Torsion Dynamometer?

Polar Moment of Inertia of Shaft for Torsion Dynamometer evaluator uses Polar Moment of Inertia of Shaft = (Total Torque*Shaft Length)/(Modulus of Rigidity*Angle of Twist) to evaluate the Polar Moment of Inertia of Shaft, Polar Moment of Inertia of Shaft for Torsion Dynamometer formula is defined as a measure of the shaft's resistance to twisting or torsion, which is essential in determining the torque and angular displacement of a rotating shaft in a dynamometer. Polar Moment of Inertia of Shaft is denoted by J symbol.

How to evaluate Polar Moment of Inertia of Shaft for Torsion Dynamometer using this online evaluator? To use this online evaluator for Polar Moment of Inertia of Shaft for Torsion Dynamometer, enter Total Torque (T), Shaft Length (L_shaft), Modulus of Rigidity (G) & Angle of Twist (θ) and hit the calculate button.

FAQs on Polar Moment of Inertia of Shaft for Torsion Dynamometer

What is the formula to find Polar Moment of Inertia of Shaft for Torsion Dynamometer?

The formula of Polar Moment of Inertia of Shaft for Torsion Dynamometer is expressed as Polar Moment of Inertia of Shaft = (Total Torque*Shaft Length)/(Modulus of Rigidity*Angle of Twist). Here is an example- 0.096127 = (13*0.42)/(40*1.517).

How to calculate Polar Moment of Inertia of Shaft for Torsion Dynamometer?

With Total Torque (T), Shaft Length (L_shaft), Modulus of Rigidity (G) & Angle of Twist (θ) we can find Polar Moment of Inertia of Shaft for Torsion Dynamometer using the formula - Polar Moment of Inertia of Shaft = (Total Torque*Shaft Length)/(Modulus of Rigidity*Angle of Twist).

What are the other ways to Calculate Polar Moment of Inertia of Shaft?

Here are the different ways to Calculate Polar Moment of Inertia of Shaft-

Polar Moment of Inertia of Shaft=pi/32*(Shaft Outer Diameter^4-Shaft Inner Diameter^4)
Polar Moment of Inertia of Shaft=pi/32*Shaft Diameter^4

Can the Polar Moment of Inertia of Shaft for Torsion Dynamometer be negative?

No, the Polar Moment of Inertia of Shaft for Torsion Dynamometer, measured in Second Moment of Area cannot be negative.

Which unit is used to measure Polar Moment of Inertia of Shaft for Torsion Dynamometer?

Polar Moment of Inertia of Shaft for Torsion Dynamometer is usually measured using the Meter⁴[m⁴] for Second Moment of Area. Centimeter⁴[m⁴], Millimeter⁴[m⁴] are the few other units in which Polar Moment of Inertia of Shaft for Torsion Dynamometer can be measured.

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Polar Moment of Inertia of Shaft for Torsion Dynamometer Formula

​GoPolar Moment of Inertia of Shaft for Hollow Shaft for Torsion Dynamometer Formula

​GoPolar Moment of Inertia of Shaft for Solid Shaft for Torsion Dynamometer Formula

Polar Moment of Inertia of Shaft for Torsion Dynamometer Example

Polar Moment of Inertia of Shaft for Torsion Dynamometer Solution

Polar Moment of Inertia of Shaft for Torsion Dynamometer Formula Elements

Other Formulas to find Polar Moment of Inertia of Shaft

Other formulas in Dynamometer category

How to Evaluate Polar Moment of Inertia of Shaft for Torsion Dynamometer?

FAQs on Polar Moment of Inertia of Shaft for Torsion Dynamometer

Variable Name

GoPolar Moment of Inertia of Shaft for Hollow Shaft for Torsion Dynamometer Formula

GoPolar Moment of Inertia of Shaft for Solid Shaft for Torsion Dynamometer Formula