Radius of shaft given polar moment of inertia Calculator

✖Maximum Shear Stress on Shaft that acts coplanar with a cross-section of material arises due to shear forces.ⓘ Maximum Shear Stress on Shaft [𝜏_max]			+10% -10%
✖Polar Moment of Inertia of shaft is the measure of object resistance to torsion.ⓘ Polar Moment of Inertia of shaft [J_shaft]			+10% -10%
✖Torque Exerted on Wheel is described as the turning effect of force on the axis of rotation. In brief, it is a moment of force. It is characterized by τ.ⓘ Torque Exerted on Wheel [τ]			+10% -10%

✖Radius of shaft is the distance between the center and the circumference of the shaft.ⓘ Radius of shaft given polar moment of inertia [R_shaft]

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Radius of shaft given polar moment of inertia Solution

STEP 0: Pre-Calculation Summary

Formula Used

Radius of Shaft = (Maximum Shear Stress on Shaft*Polar Moment of Inertia of shaft)/Torque Exerted on Wheel
R_shaft = (𝜏_max*J_shaft)/τ
This formula uses 4 Variables

Variables Used

Radius of Shaft - (Measured in Meter) - Radius of shaft is the distance between the center and the circumference of the shaft.
Maximum Shear Stress on Shaft - (Measured in Pascal) - Maximum Shear Stress on Shaft that acts coplanar with a cross-section of material arises due to shear forces.
Polar Moment of Inertia of shaft - (Measured in Meter⁴) - Polar Moment of Inertia of shaft is the measure of object resistance to torsion.
Torque Exerted on Wheel - (Measured in Newton Meter) - Torque Exerted on Wheel is described as the turning effect of force on the axis of rotation. In brief, it is a moment of force. It is characterized by τ.

STEP 1: Convert Input(s) to Base Unit

Maximum Shear Stress on Shaft: 0.0001 Megapascal --> 100 Pascal (Check conversion here)
Polar Moment of Inertia of shaft: 10 Meter⁴ --> 10 Meter⁴ No Conversion Required
Torque Exerted on Wheel: 50 Newton Meter --> 50 Newton Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

R_shaft = (𝜏_max*J_shaft)/τ --> (100*10)/50

Evaluating ... ...

R_shaft = 20

STEP 3: Convert Result to Output's Unit

20 Meter -->20000 Millimeter (Check conversion here)

FINAL ANSWER

20000 Millimeter <-- Radius of Shaft

(Calculation completed in 00.004 seconds)

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Home » Physics » Strength of Materials » Torsion of Shafts And Springs » Mechanical » Expression for Torque in terms of Polar Moment of Inertia » Radius of shaft given polar moment of inertia

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National Institute Of Technology (NIT), Hamirpur

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< Expression for Torque in terms of Polar Moment of Inertia Calculators

Modulus of Rigidity of Shaft given Torque Transmitted and Polar Moment of Inertia

LaTeX Go Modulus of Rigidity = (Torque Exerted on Wheel*Length of Shaft)/(Angle of twist*Polar Moment of Inertia of shaft)

Polar Moment of Inertia of Shaft given Torque Transmitted and Modulus of Rigidity

LaTeX Go Polar Moment of Inertia of shaft = (Torque Exerted on Wheel*Length of Shaft)/(Modulus of Rigidity*Angle of twist)

Angle of Twist for Shaft given Polar Moment of Inertia and Modulus of Rigidity

LaTeX Go Angle of twist = (Torque Exerted on Wheel*Length of Shaft)/(Modulus of Rigidity*Polar Moment of Inertia of shaft)

Length of Shaft given Polar Moment of Inertia and Modulus of Rigidity

LaTeX Go Length of Shaft = (Modulus of Rigidity*Angle of twist*Polar Moment of Inertia of shaft)/Torque Exerted on Wheel

Radius of shaft given polar moment of inertia Formula

LaTeX Go

Radius of Shaft = (Maximum Shear Stress on Shaft*Polar Moment of Inertia of shaft)/Torque Exerted on Wheel
R_shaft = (𝜏_max*J_shaft)/τ

What is difference between moment of inertia and polar moment of inertia?

The main difference between the moment of inertia and the polar moment of inertia is that the moment of inertia measures how an object resists angular acceleration, whereas the polar moment of inertia measures how an object resists torsion.

How to Calculate Radius of shaft given polar moment of inertia?

Radius of shaft given polar moment of inertia calculator uses Radius of Shaft = (Maximum Shear Stress on Shaft*Polar Moment of Inertia of shaft)/Torque Exerted on Wheel to calculate the Radius of Shaft, Radius of shaft given polar moment of inertia is defined as the distance from the center outwards. Radius of Shaft is denoted by R_shaft symbol.

How to calculate Radius of shaft given polar moment of inertia using this online calculator? To use this online calculator for Radius of shaft given polar moment of inertia, enter Maximum Shear Stress on Shaft (𝜏_max), Polar Moment of Inertia of shaft (J_shaft) & Torque Exerted on Wheel (τ) and hit the calculate button. Here is how the Radius of shaft given polar moment of inertia calculation can be explained with given input values -> 2E+7 = (100*10)/50.

FAQ

What is Radius of shaft given polar moment of inertia?

Radius of shaft given polar moment of inertia is defined as the distance from the center outwards and is represented as R_shaft = (𝜏_max*J_shaft)/τ or Radius of Shaft = (Maximum Shear Stress on Shaft*Polar Moment of Inertia of shaft)/Torque Exerted on Wheel. Maximum Shear Stress on Shaft that acts coplanar with a cross-section of material arises due to shear forces, Polar Moment of Inertia of shaft is the measure of object resistance to torsion & Torque Exerted on Wheel is described as the turning effect of force on the axis of rotation. In brief, it is a moment of force. It is characterized by τ.

How to calculate Radius of shaft given polar moment of inertia?

Radius of shaft given polar moment of inertia is defined as the distance from the center outwards is calculated using Radius of Shaft = (Maximum Shear Stress on Shaft*Polar Moment of Inertia of shaft)/Torque Exerted on Wheel. To calculate Radius of shaft given polar moment of inertia, you need Maximum Shear Stress on Shaft (𝜏_max), Polar Moment of Inertia of shaft (J_shaft) & Torque Exerted on Wheel (τ). With our tool, you need to enter the respective value for Maximum Shear Stress on Shaft, Polar Moment of Inertia of shaft & Torque Exerted on Wheel 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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