Polar Moment of Inertia of Shaft for Torsion Dynamometer Calculator

✖Total Torque is the rotational force that causes an object to rotate, measured by a dynamometer, typically in units of newton-meters or foot-pounds.ⓘ Total Torque [T]			+10% -10%
✖Shaft Length is the distance from the dynamometer's rotating shaft to the point of measurement, typically used to calculate torque and power output.ⓘ Shaft Length [L_shaft]			+10% -10%
✖Modulus of Rigidity is the measure of the stiffness of a material, determining the amount of stress required to produce a unit deformation.ⓘ Modulus of Rigidity [G]			+10% -10%
✖Angle of Twist is the rotational deformation of a shaft measured by a dynamometer, which is used to calculate the torque or rotational force.ⓘ Angle of Twist [θ]			+10% -10%

✖Polar Moment of Inertia of Shaft is a measure of an object's resistance to changes in its rotation, important in dynamometer applications.ⓘ Polar Moment of Inertia of Shaft for Torsion Dynamometer [J]

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Polar Moment of Inertia of Shaft for Torsion Dynamometer Solution

STEP 0: Pre-Calculation Summary

Formula Used

Polar Moment of Inertia of Shaft = (Total Torque*Shaft Length)/(Modulus of Rigidity*Angle of Twist)
J = (T*L_shaft)/(G*θ)
This formula uses 5 Variables

Variables Used

Polar Moment of Inertia of Shaft - (Measured in Meter⁴) - Polar Moment of Inertia of Shaft is a measure of an object's resistance to changes in its rotation, important in dynamometer applications.
Total Torque - (Measured in Newton Meter) - Total Torque is the rotational force that causes an object to rotate, measured by a dynamometer, typically in units of newton-meters or foot-pounds.
Shaft Length - (Measured in Meter) - Shaft Length is the distance from the dynamometer's rotating shaft to the point of measurement, typically used to calculate torque and power output.
Modulus of Rigidity - (Measured in Pascal) - Modulus of Rigidity is the measure of the stiffness of a material, determining the amount of stress required to produce a unit deformation.
Angle of Twist - (Measured in Radian) - Angle of Twist is the rotational deformation of a shaft measured by a dynamometer, which is used to calculate the torque or rotational force.

STEP 1: Convert Input(s) to Base Unit

Total Torque: 13 Newton Meter --> 13 Newton Meter No Conversion Required
Shaft Length: 0.42 Meter --> 0.42 Meter No Conversion Required
Modulus of Rigidity: 40 Newton per Square Meter --> 40 Pascal (Check conversion here)
Angle of Twist: 1.517 Radian --> 1.517 Radian No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

J = (T*L_shaft)/(G*θ) --> (13*0.42)/(40*1.517)

Evaluating ... ...

J = 0.0899802241265656

STEP 3: Convert Result to Output's Unit

0.0899802241265656 Meter⁴ --> No Conversion Required

FINAL ANSWER

0.0899802241265656 ≈ 0.08998 Meter⁴ <-- Polar Moment of Inertia of Shaft

(Calculation completed in 00.004 seconds)

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Polar Moment of Inertia of Shaft for Torsion Dynamometer Formula

LaTeX Go

Polar Moment of Inertia of Shaft = (Total Torque*Shaft Length)/(Modulus of Rigidity*Angle of Twist)
J = (T*L_shaft)/(G*θ)

What is Polar Moment of Inertia of Shaft?

The polar moment of inertia of a shaft is a measure of its resistance to torsional deformation when subjected to torque. It depends on the shaft's geometry, particularly its cross-sectional shape and size. A larger polar moment of inertia indicates greater stiffness and resistance to twisting. It is crucial in determining the shaft's strength and ability to withstand torsional loads without excessive twisting.

How to Calculate Polar Moment of Inertia of Shaft for Torsion Dynamometer?

Polar Moment of Inertia of Shaft for Torsion Dynamometer calculator uses Polar Moment of Inertia of Shaft = (Total Torque*Shaft Length)/(Modulus of Rigidity*Angle of Twist) to calculate the Polar Moment of Inertia of Shaft, Polar Moment of Inertia of Shaft for Torsion Dynamometer formula is defined as a measure of the shaft's resistance to twisting or torsion, which is essential in determining the torque and angular displacement of a rotating shaft in a dynamometer. Polar Moment of Inertia of Shaft is denoted by J symbol.

How to calculate Polar Moment of Inertia of Shaft for Torsion Dynamometer using this online calculator? To use this online calculator for Polar Moment of Inertia of Shaft for Torsion Dynamometer, enter Total Torque (T), Shaft Length (L_shaft), Modulus of Rigidity (G) & Angle of Twist (θ) and hit the calculate button. Here is how the Polar Moment of Inertia of Shaft for Torsion Dynamometer calculation can be explained with given input values -> 0.096127 = (13*0.42)/(40*1.517).

FAQ

What is Polar Moment of Inertia of Shaft for Torsion Dynamometer?

Polar Moment of Inertia of Shaft for Torsion Dynamometer formula is defined as a measure of the shaft's resistance to twisting or torsion, which is essential in determining the torque and angular displacement of a rotating shaft in a dynamometer and is represented as J = (T*L_shaft)/(G*θ) or Polar Moment of Inertia of Shaft = (Total Torque*Shaft Length)/(Modulus of Rigidity*Angle of Twist). Total Torque is the rotational force that causes an object to rotate, measured by a dynamometer, typically in units of newton-meters or foot-pounds, Shaft Length is the distance from the dynamometer's rotating shaft to the point of measurement, typically used to calculate torque and power output, Modulus of Rigidity is the measure of the stiffness of a material, determining the amount of stress required to produce a unit deformation & Angle of Twist is the rotational deformation of a shaft measured by a dynamometer, which is used to calculate the torque or rotational force.

How to calculate Polar Moment of Inertia of Shaft for Torsion Dynamometer?

Polar Moment of Inertia of Shaft for Torsion Dynamometer formula is defined as a measure of the shaft's resistance to twisting or torsion, which is essential in determining the torque and angular displacement of a rotating shaft in a dynamometer is calculated using Polar Moment of Inertia of Shaft = (Total Torque*Shaft Length)/(Modulus of Rigidity*Angle of Twist). To calculate Polar Moment of Inertia of Shaft for Torsion Dynamometer, you need Total Torque (T), Shaft Length (L_shaft), Modulus of Rigidity (G) & Angle of Twist (θ). With our tool, you need to enter the respective value for Total Torque, Shaft Length, Modulus of Rigidity & Angle of Twist 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 of Shaft?

In this formula, Polar Moment of Inertia of Shaft uses Total Torque, Shaft Length, Modulus of Rigidity & Angle of Twist. We can use 2 other way(s) to calculate the same, which is/are as follows -

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

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