Radius of Shaft using Polar Modulus Solution

STEP 0: Pre-Calculation Summary
Formula Used
Radius of Shaft = Polar Moment of Inertia/Polar Modulus
R = J/Zp
This formula uses 3 Variables
Variables Used
Radius of Shaft - (Measured in Millimeter) - The Radius of Shaft is the line segment extending from the center of a circle or sphere to the circumference or bounding surface.
Polar Moment of Inertia - (Measured in Meter⁴) - 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.
Polar Modulus - (Measured in Cubic Meter) - 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.
STEP 1: Convert Input(s) to Base Unit
Polar Moment of Inertia: 0.0041 Meter⁴ --> 0.0041 Meter⁴ No Conversion Required
Polar Modulus: 0.0045 Cubic Meter --> 0.0045 Cubic Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
R = J/Zp --> 0.0041/0.0045
Evaluating ... ...
R = 0.911111111111111
STEP 3: Convert Result to Output's Unit
0.000911111111111111 Meter -->0.911111111111111 Millimeter (Check conversion here)
FINAL ANSWER
0.911111111111111 0.911111 Millimeter <-- Radius of Shaft
(Calculation completed in 00.004 seconds)

Credits

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National Institute Of Technology (NIT), Hamirpur
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9 Polar Modulus Calculators

Inner diameter of Hollow Shaft using Polar Modulus
Go Inner Dia of Shaft = ((Outer Diameter of Shaft^4)-((Polar Modulus*16*Outer Diameter of Shaft)/pi))^(1/4)
Polar Modulus of Hollow Shaft
Go Polar Modulus = (pi*((Outer Diameter of Shaft^4)-(Inner Dia of Shaft^4)))/(16*Outer Diameter of Shaft)
Polar Moment of Inertia of Hollow Shaft
Go Polar Moment of Inertia = pi/32*(Outer Diameter of Shaft^4-Inner Dia of Shaft^4)
Polar Moment of Inertia using Polar Modulus
Go Polar Moment of Inertia = Radius of Shaft*Polar Modulus
Radius of Shaft using Polar Modulus
Go Radius of Shaft = Polar Moment of Inertia/Polar Modulus
Polar Modulus
Go Polar Modulus = Polar Moment of Inertia/Radius of Shaft
Polar Moment of Inertia of Solid Shaft
Go Polar Moment of Inertia = (pi*Dia of Shaft^4)/32
Diameter of Solid Shaft with known Polar Modulus
Go Dia of Shaft = ((16*Polar Modulus)/pi)^(1/3)
Polar Modulus of Solid Shaft
Go Polar Modulus = (pi*Dia of Shaft^3)/16

18 Torsion Calculators

Shaft length for given maximum permissible shear stress and modulus of rigidity
Go Length of Shaft = (Modulus of Rigidity*(Angle of Twist)*Radius of Shaft)/Maximum Shear Stress
Maximum permissible shear stress for given Radius and modulus of rigidity
Go Maximum Shear Stress = (Modulus of Rigidity*(Angle of Twist)*Radius of Shaft)/Length of Shaft
Modulus of rigidity given maximum permissible shear stress
Go Modulus of Rigidity = (Maximum Shear Stress*Length of Shaft)/(Angle of Twist*Radius of Shaft)
Twist angle given maximum permissible shear stress
Go Angle of Twist = (Maximum Shear Stress*Length of Shaft)/(Radius of Shaft*Modulus of Rigidity)
Shaft length for given Polar MOI, Twisting Moment, Modulus of rigidity, and Twist angle
Go Length of Shaft = (Modulus of Rigidity*(Angle of Twist)*Polar Moment of Inertia)/Torque
Twist angle given Shaft length and modulus of rigidity
Go Angle of Twist = (Torque*Length of Shaft)/(Polar Moment of Inertia*Modulus of Rigidity)
Polar moment of inertia
Go Polar Moment of Inertia = (Torque*Length of Shaft)/(Angle of Twist*Modulus of Rigidity)
Modulus of rigidity
Go Modulus of Rigidity = (Torque*Length of Shaft)/(Angle of Twist*Polar Moment of Inertia)
Twisting Moment given Polar MOI and Twist Angle
Go Torque = (Modulus of Rigidity*Angle of Twist*Polar Moment of Inertia)/Length of Shaft
Polar Moment of Inertia of Hollow Shaft
Go Polar Moment of Inertia = pi/32*(Outer Diameter of Shaft^4-Inner Dia of Shaft^4)
Twisting Moment given Maximum Permissible Shear Stress
Go Torque = (Polar Moment of Inertia*Maximum Shear Stress)/Radius of Shaft
Polar Moment of Inertia given twisting moment along with maximum permissible shear stress
Go Polar Moment of Inertia = Torque*Radius of Shaft/Maximum Shear Stress
Radius given Twisting moment and Polar Moment of Inertia of shaft
Go Radius of Shaft = Maximum Shear Stress*Polar Moment of Inertia/Torque
Radius with known Maximum permissible shear stress
Go Radius of Shaft = Maximum Shear Stress*Polar Moment of Inertia/Torque
Maximum permissible shear stress
Go Maximum Shear Stress = Torque*Radius of Shaft/Polar Moment of Inertia
Radius given Torsional Section Modulus
Go Radius of Shaft = Polar Moment of Inertia/Polar Modulus
Radius of Shaft using Polar Modulus
Go Radius of Shaft = Polar Moment of Inertia/Polar Modulus
Torsional Section Modulus
Go Polar Modulus = Polar Moment of Inertia/Radius of Shaft

Radius of Shaft using Polar Modulus Formula

Radius of Shaft = Polar Moment of Inertia/Polar Modulus
R = J/Zp

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 using Polar Modulus?

Radius of Shaft using Polar Modulus calculator uses Radius of Shaft = Polar Moment of Inertia/Polar Modulus to calculate the Radius of Shaft, The Radius of Shaft using Polar Modulus formula is defined as the distance from the center outwards. Radius of Shaft is denoted by R symbol.

How to calculate Radius of Shaft using Polar Modulus using this online calculator? To use this online calculator for Radius of Shaft using Polar Modulus, enter Polar Moment of Inertia (J) & Polar Modulus (Zp) and hit the calculate button. Here is how the Radius of Shaft using Polar Modulus calculation can be explained with given input values -> 0.911111 = 0.0041/0.0045.

FAQ

What is Radius of Shaft using Polar Modulus?
The Radius of Shaft using Polar Modulus formula is defined as the distance from the center outwards and is represented as R = J/Zp or Radius of Shaft = Polar Moment of Inertia/Polar Modulus. 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 & 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.
How to calculate Radius of Shaft using Polar Modulus?
The Radius of Shaft using Polar Modulus formula is defined as the distance from the center outwards is calculated using Radius of Shaft = Polar Moment of Inertia/Polar Modulus. To calculate Radius of Shaft using Polar Modulus, you need Polar Moment of Inertia (J) & Polar Modulus (Zp). With our tool, you need to enter the respective value for Polar Moment of Inertia & Polar Modulus and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
How many ways are there to calculate Radius of Shaft?
In this formula, Radius of Shaft uses Polar Moment of Inertia & Polar Modulus. We can use 3 other way(s) to calculate the same, which is/are as follows -
  • Radius of Shaft = Maximum Shear Stress*Polar Moment of Inertia/Torque
  • Radius of Shaft = Polar Moment of Inertia/Polar Modulus
  • Radius of Shaft = Maximum Shear Stress*Polar Moment of Inertia/Torque
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