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Polar Modulus of Solid Shaft Formula

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GoPolar Modulus of Hollow Shaft Formula

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The Polar Modulus of the shaft section is equal to the ratio of the polar moment of inertia to the radius of the shaft. It is denoted by Zp. Check FAQs

Z p = \frac{π \cdot d^{3}}{16}

Z_p - Polar Modulus?d - Dia of Shaft?π - Archimedes' constant?

Polar Modulus of Solid Shaft Example

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Here is how the Polar Modulus of Solid Shaft equation looks like with Values.

Here is how the Polar Modulus of Solid Shaft equation looks like with Units.

Here is how the Polar Modulus of Solid Shaft equation looks like.

0.0045 = \frac{3.1416 \cdot {0.284}^{3}}{16}

0.0045m³ = \frac{3.1416 \cdot {0.284m}^{3}}{16}

0.0045 = \frac{3.1416 \cdot {0.284}^{3}}{16}

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Polar Modulus of Solid Shaft Solution

Follow our step by step solution on how to calculate Polar Modulus of Solid Shaft?

FIRST Step Consider the formula

Z p = \frac{π \cdot d^{3}}{16}

Next Step Substitute values of Variables

∴

Z p = \frac{π \cdot {0.284m}^{3}}{16}

Next Step Substitute values of Constants

∴

Z p = \frac{3.1416 \cdot {0.284m}^{3}}{16}

Next Step Prepare to Evaluate

∴

Z p = \frac{3.1416 \cdot {0.284}^{3}}{16}

Next Step Evaluate

∴

Z p = 0.0044976422729559m³

LAST Step Rounding Answer

∴

Z p = 0.0045m³

Polar Modulus of Solid Shaft Formula Elements

Variables

Constants

Polar Modulus

The Polar Modulus of the shaft section is equal to the ratio of the polar moment of inertia to the radius of the shaft. It is denoted by Zp.

Symbol: Z_p

Measurement: VolumeUnit: m³

Note: Value should be greater than 0.

Formulas to find Polar Modulus

Dia of Shaft

The Dia of Shaft is the diameter of the external surface of a shaft which is a rotating element in the transmitting system for transmitting power.

Symbol: d

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find 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 Modulus

Go Polar Modulus

Z p = \frac{J}{R}

Go Polar Modulus of Hollow Shaft

Z p = \frac{π \cdot (({d o}^{4}) - ({d i}^{4}))}{16 \cdot d o}

Go Polar Modulus using Maximum Twisting Moment

Z p = (\frac{T}{τ max})

Other formulas in Polar Modulus category

Go Diameter of Solid Shaft with known Polar Modulus

d = {(\frac{16 \cdot Z p}{π})}^{\frac{1}{3}}

Go Inner diameter of Hollow Shaft using Polar Modulus

d i = {(({d o}^{4}) - (\frac{Z p \cdot 16 \cdot d o}{π}))}^{\frac{1}{4}}

Go Polar Moment of Inertia using Polar Modulus

J = R \cdot Z p

Go Polar Moment of Inertia of Solid Shaft

J = \frac{π \cdot d^{4}}{32}

How to Evaluate Polar Modulus of Solid Shaft?

Polar Modulus of Solid Shaft evaluator uses Polar Modulus = (pi*Dia of Shaft^3)/16 to evaluate the Polar Modulus, The Polar Modulus of Solid Shaft formula is defined as the ratio of the polar moment of inertia to the radius of the shaft. It is also called a torsional section modulus. It is denoted by Z p. Polar Modulus is denoted by Z_p symbol.

How to evaluate Polar Modulus of Solid Shaft using this online evaluator? To use this online evaluator for Polar Modulus of Solid Shaft, enter Dia of Shaft (d) and hit the calculate button.

FAQs on Polar Modulus of Solid Shaft

What is the formula to find Polar Modulus of Solid Shaft?

The formula of Polar Modulus of Solid Shaft is expressed as Polar Modulus = (pi*Dia of Shaft^3)/16. Here is an example- 0.004498 = (pi*0.284^3)/16.

How to calculate Polar Modulus of Solid Shaft?

With Dia of Shaft (d) we can find Polar Modulus of Solid Shaft using the formula - Polar Modulus = (pi*Dia of Shaft^3)/16. This formula also uses Archimedes' constant .

What are the other ways to Calculate Polar Modulus?

Here are the different ways to Calculate Polar Modulus-

Polar Modulus=Polar Moment of Inertia/Radius of Shaft
Polar Modulus=(pi*((Outer Diameter of Shaft^4)-(Inner Dia of Shaft^4)))/(16*Outer Diameter of Shaft)
Polar Modulus=(Torque/Maximum Shear Stress)

Can the Polar Modulus of Solid Shaft be negative?

No, the Polar Modulus of Solid Shaft, measured in Volume cannot be negative.

Which unit is used to measure Polar Modulus of Solid Shaft?

Polar Modulus of Solid Shaft is usually measured using the Cubic Meter[m³] for Volume. Cubic Centimeter[m³], Cubic Millimeter[m³], Liter[m³] are the few other units in which Polar Modulus of Solid Shaft can be measured.

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