Angle of Twist for Shaft given Polar Moment of Inertia and Modulus of Rigidity Calculator

✖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.ⓘ Torque Exerted on Wheel [τ]			+10% -10%
✖The Length of Shaft is the distance between two ends of shaft.ⓘ Length of Shaft [L]			+10% -10%
✖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.ⓘ Modulus of Rigidity [C]			+10% -10%
✖Polar Moment of Inertia of shaft is the measure of object resistance to torsion.ⓘ Polar Moment of Inertia of shaft [J_shaft]			+10% -10%

✖Angle of twist is the angle through which the fixed end of a shaft rotates with respect to the free end.ⓘ Angle of Twist for Shaft given Polar Moment of Inertia and Modulus of Rigidity [θ]

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Formula

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Angle of Twist for Shaft given Polar Moment of Inertia and Modulus of Rigidity

Formula

`"θ" = ("τ"*"L")/("C"*"J"_{"shaft"})`

Example

`"4.2E^-10"=("50N*m"*"7000mm")/("84000N/mm²"*"10m⁴")`

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Angle of Twist for Shaft given Polar Moment of Inertia and Modulus of Rigidity Solution

STEP 0: Pre-Calculation Summary

Formula Used

Angle of twist = (Torque Exerted on Wheel*Length of Shaft)/(Modulus of Rigidity*Polar Moment of Inertia of shaft)
θ = (τ*L)/(C*J_shaft)
This formula uses 5 Variables

Variables Used

Angle of twist - Angle of twist is the angle through which the fixed end of a shaft rotates with respect to the free end.
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.
Length of Shaft - (Measured in Meter) - The Length of Shaft is the distance between two ends of shaft.
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.
Polar Moment of Inertia of shaft - (Measured in Meter⁴) - Polar Moment of Inertia of shaft is the measure of object resistance to torsion.

STEP 1: Convert Input(s) to Base Unit

Torque Exerted on Wheel: 50 Newton Meter --> 50 Newton Meter No Conversion Required
Length of Shaft: 7000 Millimeter --> 7 Meter (Check conversion here)
Modulus of Rigidity: 84000 Newton per Square Millimeter --> 84000000000 Pascal (Check conversion here)
Polar Moment of Inertia of shaft: 10 Meter⁴ --> 10 Meter⁴ No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

θ = (τ*L)/(C*J_shaft) --> (50*7)/(84000000000*10)

Evaluating ... ...

θ = 4.16666666666667E-10

STEP 3: Convert Result to Output's Unit

4.16666666666667E-10 --> No Conversion Required

FINAL ANSWER

4.16666666666667E-10 ≈ 4.2E-10 <-- Angle of twist

(Calculation completed in 00.004 seconds)

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Home » Physics » Strength of Materials » Torsion of Shafts And Springs » Expression for Torque in terms of Polar Moment of Inertia » Angle of Twist for Shaft given Polar Moment of Inertia and Modulus of Rigidity

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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

Angle of Twist for Shaft given Polar Moment of Inertia and Modulus of Rigidity Formula

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

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 Angle of Twist for Shaft given Polar Moment of Inertia and Modulus of Rigidity?

Angle of Twist for Shaft given Polar Moment of Inertia and Modulus of Rigidity calculator uses Angle of twist = (Torque Exerted on Wheel*Length of Shaft)/(Modulus of Rigidity*Polar Moment of Inertia of shaft) to calculate the Angle of twist, Angle of Twist for Shaft given Polar Moment of Inertia and Modulus of Rigidity is defined as the angle through which the fixed end of a shaft rotates with respect to the free end. Angle of twist is denoted by θ symbol.

How to calculate Angle of Twist for Shaft given Polar Moment of Inertia and Modulus of Rigidity using this online calculator? To use this online calculator for Angle of Twist for Shaft given Polar Moment of Inertia and Modulus of Rigidity, enter Torque Exerted on Wheel (τ), Length of Shaft (L), Modulus of Rigidity (C) & Polar Moment of Inertia of shaft (J_shaft) and hit the calculate button. Here is how the Angle of Twist for Shaft given Polar Moment of Inertia and Modulus of Rigidity calculation can be explained with given input values -> 4.2E-10 = (50*7)/(84000000000*10).

FAQ

What is Angle of Twist for Shaft given Polar Moment of Inertia and Modulus of Rigidity?

Angle of Twist for Shaft given Polar Moment of Inertia and Modulus of Rigidity is defined as the angle through which the fixed end of a shaft rotates with respect to the free end and is represented as θ = (τ*L)/(C*J_shaft) or Angle of twist = (Torque Exerted on Wheel*Length of Shaft)/(Modulus of Rigidity*Polar Moment of Inertia of shaft). 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, The Length of Shaft is the distance between two ends 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 & Polar Moment of Inertia of shaft is the measure of object resistance to torsion.

How to calculate Angle of Twist for Shaft given Polar Moment of Inertia and Modulus of Rigidity?

Angle of Twist for Shaft given Polar Moment of Inertia and Modulus of Rigidity is defined as the angle through which the fixed end of a shaft rotates with respect to the free end is calculated using Angle of twist = (Torque Exerted on Wheel*Length of Shaft)/(Modulus of Rigidity*Polar Moment of Inertia of shaft). To calculate Angle of Twist for Shaft given Polar Moment of Inertia and Modulus of Rigidity, you need Torque Exerted on Wheel (τ), Length of Shaft (L), Modulus of Rigidity (C) & Polar Moment of Inertia of shaft (J_shaft). With our tool, you need to enter the respective value for Torque Exerted on Wheel, Length of Shaft, Modulus of Rigidity & Polar Moment of Inertia of shaft 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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