Polar Moment of Inertia of Hollow Shaft Solution

STEP 0: Pre-Calculation Summary
Formula Used
Polar Moment of Inertia = pi/32*(Outer Diameter of Shaft^4-Inner Dia of Shaft^4)
J = pi/32*(do^4-di^4)
This formula uses 1 Constants, 3 Variables
Constants Used
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
Variables Used
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.
Outer Diameter of Shaft - (Measured in Meter) - Outer Diameter of Shaft is the length of the longest chord of the surface of the hollow circular shaft.
Inner Dia of Shaft - (Measured in Meter) - The Inner Dia of Shaft is defined as the Diameter that is length of the longest chord inside the hollow shaft.
STEP 1: Convert Input(s) to Base Unit
Outer Diameter of Shaft: 700 Millimeter --> 0.7 Meter (Check conversion here)
Inner Dia of Shaft: 0.688 Meter --> 0.688 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
J = pi/32*(do^4-di^4) --> pi/32*(0.7^4-0.688^4)
Evaluating ... ...
J = 0.00157525912252214
STEP 3: Convert Result to Output's Unit
0.00157525912252214 Meter⁴ --> No Conversion Required
FINAL ANSWER
0.00157525912252214 0.001575 Meter⁴ <-- Polar Moment of Inertia
(Calculation completed in 00.004 seconds)

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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

Polar Moment of Inertia of Hollow Shaft Formula

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

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 Polar Moment of Inertia of Hollow Shaft?

Polar Moment of Inertia of Hollow Shaft calculator uses Polar Moment of Inertia = pi/32*(Outer Diameter of Shaft^4-Inner Dia of Shaft^4) to calculate 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 calculate Polar Moment of Inertia of Hollow Shaft using this online calculator? To use this online calculator for Polar Moment of Inertia of Hollow Shaft, enter Outer Diameter of Shaft (do) & Inner Dia of Shaft (di) and hit the calculate button. Here is how the Polar Moment of Inertia of Hollow Shaft calculation can be explained with given input values -> 0.001575 = pi/32*(0.7^4-0.688^4).

FAQ

What is Polar Moment of Inertia of Hollow Shaft?
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 and is represented as J = pi/32*(do^4-di^4) or Polar Moment of Inertia = pi/32*(Outer Diameter of Shaft^4-Inner Dia of Shaft^4). Outer Diameter of Shaft is the length of the longest chord of the surface of the hollow circular shaft & The Inner Dia of Shaft is defined as the Diameter that is length of the longest chord inside the hollow shaft.
How to calculate Polar Moment of Inertia of Hollow Shaft?
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 is calculated using Polar Moment of Inertia = pi/32*(Outer Diameter of Shaft^4-Inner Dia of Shaft^4). To calculate Polar Moment of Inertia of Hollow Shaft, you need Outer Diameter of Shaft (do) & Inner Dia of Shaft (di). With our tool, you need to enter the respective value for Outer Diameter of Shaft & Inner Dia of Shaft 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 Polar Moment of Inertia?
In this formula, Polar Moment of Inertia uses Outer Diameter of Shaft & Inner Dia of Shaft. We can use 4 other way(s) to calculate the same, which is/are as follows -
  • Polar Moment of Inertia = Radius of Shaft*Polar Modulus
  • Polar Moment of Inertia = (pi*Dia of Shaft^4)/32
  • 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)
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