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
Rshaft = (𝜏max*Jshaft)/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
Rshaft = (𝜏max*Jshaft)/τ --> (100*10)/50
Evaluating ... ...
Rshaft = 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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11 Expression for Torque in terms of Polar Moment of Inertia Calculators

Modulus of Rigidity of Shaft given Torque Transmitted and Polar Moment of Inertia
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
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
Go Angle of twist = (Torque Exerted on Wheel*Length of Shaft)/(Modulus of Rigidity*Polar Moment of Inertia of shaft)
Torque Transmitted by Shaft given Polar Moment of Inertia and Modulus of Rigidity
Go Torque Exerted on Wheel = (Modulus of Rigidity*Angle of twist*Polar Moment of Inertia of shaft)/Length of Shaft
Length of Shaft given Polar Moment of Inertia and Modulus of Rigidity
Go Length of Shaft = (Modulus of Rigidity*Angle of twist*Polar Moment of Inertia of shaft)/Torque Exerted on Wheel
Polar moment of inertia of shaft given torque transmitted by shaft
Go Polar Moment of Inertia of shaft = (Torque Exerted on Wheel*Radius of Shaft)/Maximum Shear Stress on Shaft
Maximum shear stress in shaft given polar moment of inertia
Go Maximum Shear Stress on Shaft = (Torque Exerted on Wheel*Radius of Shaft)/Polar Moment of Inertia of shaft
Torque transmitted by shaft given polar moment of inertia
Go Torque Exerted on Wheel = (Maximum Shear Stress on Shaft*Polar Moment of Inertia of shaft)/Radius of Shaft
Radius of shaft given polar moment of inertia
Go Radius of Shaft = (Maximum Shear Stress on Shaft*Polar Moment of Inertia of shaft)/Torque Exerted on Wheel
Diameter of shaft given polar moment of inertia of shaft
Go Diameter of Shaft = ((32*Polar Moment of Inertia of shaft)/pi)^(1/4)
Polar moment of inertia of shaft
Go Polar Moment of Inertia of shaft = (pi*Diameter of Shaft^4)/32

Radius of shaft given polar moment of inertia Formula

Radius of Shaft = (Maximum Shear Stress on Shaft*Polar Moment of Inertia of shaft)/Torque Exerted on Wheel
Rshaft = (𝜏max*Jshaft)/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 Rshaft 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 (𝜏max), Polar Moment of Inertia of shaft (Jshaft) & 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 Rshaft = (𝜏max*Jshaft)/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 (𝜏max), Polar Moment of Inertia of shaft (Jshaft) & 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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