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

STEP 0: Pre-Calculation Summary
Formula Used
Torque Exerted on Wheel = (Modulus of Rigidity*Angle of twist*Polar Moment of Inertia of shaft)/Length of Shaft
τ = (C*θ*Jshaft)/L
This formula uses 5 Variables
Variables Used
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.
Modulus of Rigidity - (Measured in Pascal) - Modulus of Rigidity is the elastic coefficient when a shear force is applied resulting in lateral deformation. It gives us a measure of how rigid a body is.
Angle of twist - Angle of twist is the angle through which the fixed end of a shaft rotates with respect to the free end.
Polar Moment of Inertia of shaft - (Measured in Meter⁴) - Polar Moment of Inertia of shaft is the measure of object resistance to torsion.
Length of Shaft - (Measured in Meter) - The Length of Shaft is the distance between two ends of shaft.
STEP 1: Convert Input(s) to Base Unit
Modulus of Rigidity: 84000 Newton per Square Millimeter --> 84000000000 Pascal (Check conversion here)
Angle of twist: 30 --> No Conversion Required
Polar Moment of Inertia of shaft: 10 Meter⁴ --> 10 Meter⁴ No Conversion Required
Length of Shaft: 7000 Millimeter --> 7 Meter (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
τ = (C*θ*Jshaft)/L --> (84000000000*30*10)/7
Evaluating ... ...
τ = 3600000000000
STEP 3: Convert Result to Output's Unit
3600000000000 Newton Meter --> No Conversion Required
FINAL ANSWER
3600000000000 3.6E+12 Newton Meter <-- Torque Exerted on Wheel
(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

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

Torque Exerted on Wheel = (Modulus of Rigidity*Angle of twist*Polar Moment of Inertia of shaft)/Length of Shaft
τ = (C*θ*Jshaft)/L

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

Torque Transmitted by Shaft given Polar Moment of Inertia and Modulus of Rigidity calculator uses Torque Exerted on Wheel = (Modulus of Rigidity*Angle of twist*Polar Moment of Inertia of shaft)/Length of Shaft to calculate the Torque Exerted on Wheel, Torque Transmitted by Shaft given Polar Moment of Inertia and Modulus of Rigidity is defined as the measure of the force that can cause an object to rotate about an axis. Torque Exerted on Wheel is denoted by τ symbol.

How to calculate Torque Transmitted by Shaft given Polar Moment of Inertia and Modulus of Rigidity using this online calculator? To use this online calculator for Torque Transmitted by Shaft given Polar Moment of Inertia and Modulus of Rigidity, enter Modulus of Rigidity (C), Angle of twist (θ), Polar Moment of Inertia of shaft (Jshaft) & Length of Shaft (L) and hit the calculate button. Here is how the Torque Transmitted by Shaft given Polar Moment of Inertia and Modulus of Rigidity calculation can be explained with given input values -> 3.6E+12 = (84000000000*30*10)/7.

FAQ

What is Torque Transmitted by Shaft given Polar Moment of Inertia and Modulus of Rigidity?
Torque Transmitted by Shaft given Polar Moment of Inertia and Modulus of Rigidity is defined as the measure of the force that can cause an object to rotate about an axis and is represented as τ = (C*θ*Jshaft)/L or Torque Exerted on Wheel = (Modulus of Rigidity*Angle of twist*Polar Moment of Inertia of shaft)/Length of Shaft. Modulus of Rigidity is the elastic coefficient when a shear force is applied resulting in lateral deformation. It gives us a measure of how rigid a body is, Angle of twist is the angle through which the fixed end of a shaft rotates with respect to the free end, Polar Moment of Inertia of shaft is the measure of object resistance to torsion & The Length of Shaft is the distance between two ends of shaft.
How to calculate Torque Transmitted by Shaft given Polar Moment of Inertia and Modulus of Rigidity?
Torque Transmitted by Shaft given Polar Moment of Inertia and Modulus of Rigidity is defined as the measure of the force that can cause an object to rotate about an axis is calculated using Torque Exerted on Wheel = (Modulus of Rigidity*Angle of twist*Polar Moment of Inertia of shaft)/Length of Shaft. To calculate Torque Transmitted by Shaft given Polar Moment of Inertia and Modulus of Rigidity, you need Modulus of Rigidity (C), Angle of twist (θ), Polar Moment of Inertia of shaft (Jshaft) & Length of Shaft (L). With our tool, you need to enter the respective value for Modulus of Rigidity, Angle of twist, Polar Moment of Inertia of shaft & Length 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 Torque Exerted on Wheel?
In this formula, Torque Exerted on Wheel uses Modulus of Rigidity, Angle of twist, Polar Moment of Inertia of shaft & Length of Shaft. We can use 1 other way(s) to calculate the same, which is/are as follows -
  • Torque Exerted on Wheel = (Maximum Shear Stress on Shaft*Polar Moment of Inertia of shaft)/Radius of Shaft
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