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Polar Moment of Inertia of Hollow Shaft Formula

GoPolar Moment of Inertia given twisting moment along with maximum permissible shear stress Formula

GoPolar moment of inertia Formula

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Polar Moment of Inertia is the moment of inertia of a cross-section with respect to its polar axis, which is an axis at right angles to the plane of the cross-section. Check FAQs

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

J - Polar Moment of Inertia?d_o - Outer Diameter of Shaft?d_i - Inner Dia of Shaft?π - Archimedes' constant?

Polar Moment of Inertia of Hollow Shaft Example

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Here is how the Polar Moment of Inertia of Hollow Shaft equation looks like with Values.

Here is how the Polar Moment of Inertia of Hollow Shaft equation looks like with Units.

Here is how the Polar Moment of Inertia of Hollow Shaft equation looks like.

0.0016 = \frac{3.1416}{32} \cdot (700^{4} - {0.688}^{4})

0.0016m⁴ = \frac{3.1416}{32} \cdot ({700mm}^{4} - {0.688m}^{4})

0.0016 = \frac{3.1416}{32} \cdot (700^{4} - {0.688}^{4})

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Polar Moment of Inertia of Hollow Shaft Solution

Follow our step by step solution on how to calculate Polar Moment of Inertia of Hollow Shaft?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

J = \frac{π}{32} \cdot ({700mm}^{4} - {0.688m}^{4})

Next Step Substitute values of Constants

∴

J = \frac{3.1416}{32} \cdot ({700mm}^{4} - {0.688m}^{4})

Next Step Convert Units

∴

J = \frac{3.1416}{32} \cdot ({0.7m}^{4} - {0.688m}^{4})

Next Step Prepare to Evaluate

∴

J = \frac{3.1416}{32} \cdot ({0.7}^{4} - {0.688}^{4})

Next Step Evaluate

∴

J = 0.00157525912252214m⁴

LAST Step Rounding Answer

∴

J = 0.0016m⁴

Polar Moment of Inertia of Hollow Shaft Formula Elements

Variables

Constants

Polar Moment of Inertia

Polar Moment of Inertia is the moment of inertia of a cross-section with respect to its polar axis, which is an axis at right angles to the plane of the cross-section.

Symbol: J

Measurement: Second Moment of AreaUnit: m⁴

Note: Value should be greater than 0.

Formulas to find Polar Moment of Inertia

Outer Diameter of Shaft

Outer Diameter of Shaft is the length of the longest chord of the surface of the hollow circular shaft.

Symbol: d_o

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Outer Diameter of Shaft

Inner Dia of Shaft

The Inner Dia of Shaft is defined as the Diameter that is length of the longest chord inside the hollow shaft.

Symbol: d_i

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Inner Dia of Shaft

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

Other Formulas to find Polar Moment of Inertia

Go Polar Moment of Inertia given twisting moment along with maximum permissible shear stress

J = T \cdot \frac{R}{τ max}

Go Polar moment of inertia

J = \frac{T \cdot L shaft}{θ \cdot G Torsion}

Other formulas in Polar Modulus category

Go Twisting Moment given Maximum Permissible Shear Stress

T = \frac{J \cdot τ max}{R}

Go Maximum permissible shear stress

τ max = T \cdot \frac{R}{J}

Go Radius with known Maximum permissible shear stress

R = τ max \cdot \frac{J}{T}

Go Maximum permissible shear stress for given Radius and modulus of rigidity

τ max = \frac{G Torsion \cdot (θ) \cdot R}{L shaft}

How to Evaluate Polar Moment of Inertia of Hollow Shaft?

Polar Moment of Inertia of Hollow Shaft evaluator uses Polar Moment of Inertia = pi/32*(Outer Diameter of Shaft^4-Inner Dia of Shaft^4) to evaluate the Polar Moment of Inertia, The Polar Moment of Inertia of Hollow Shaft formula is defined as a quantity used to describe resistance to torsional deformation (deflection), in cylindrical objects (or segments of the cylindrical object) with an invariant cross-section and no significant warping or out-of-plane deformation. Polar Moment of Inertia is denoted by J symbol.

How to evaluate Polar Moment of Inertia of Hollow Shaft using this online evaluator? To use this online evaluator for Polar Moment of Inertia of Hollow Shaft, enter Outer Diameter of Shaft (d_o) & Inner Dia of Shaft (d_i) and hit the calculate button.

FAQs on Polar Moment of Inertia of Hollow Shaft

What is the formula to find Polar Moment of Inertia of Hollow Shaft?

The formula of Polar Moment of Inertia of Hollow Shaft is expressed as Polar Moment of Inertia = pi/32*(Outer Diameter of Shaft^4-Inner Dia of Shaft^4). Here is an example- 0.001575 = pi/32*(0.7^4-0.688^4).

How to calculate Polar Moment of Inertia of Hollow Shaft?

With Outer Diameter of Shaft (d_o) & Inner Dia of Shaft (d_i) we can find Polar Moment of Inertia of Hollow Shaft using the formula - Polar Moment of Inertia = pi/32*(Outer Diameter of Shaft^4-Inner Dia of Shaft^4). This formula also uses Archimedes' constant .

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

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

Polar Moment of Inertia=Torque*Radius of Shaft/Maximum Shear Stress
Polar Moment of Inertia=(Torque*Length of Shaft)/(Angle of Twist*Modulus of Rigidity)

Can the Polar Moment of Inertia of Hollow Shaft be negative?

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

Which unit is used to measure Polar Moment of Inertia of Hollow Shaft?

Polar Moment of Inertia of Hollow Shaft 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 Hollow Shaft can be measured.

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