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Angle of twist of shaft in radians given torque, length of shaft, polar moment of inertia Formula

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Angle of twist of shaft is the angle through which the fixed end of a shaft rotates with respect to the free end. Check FAQs

θ = \frac{τ \cdot l}{J \cdot C}

θ - Angle of twist of shaft?τ - Torsional moment on shaft?l - Length of Shaft?J - Polar moment of inertia for circular section?C - Modulus of Rigidity?

Angle of twist of shaft in radians given torque, length of shaft, polar moment of inertia Example

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Here is how the Angle of twist of shaft in radians given torque, length of shaft, polar moment of inertia equation looks like with Values.

Here is how the Angle of twist of shaft in radians given torque, length of shaft, polar moment of inertia equation looks like with Units.

Here is how the Angle of twist of shaft in radians given torque, length of shaft, polar moment of inertia equation looks like.

0.0176 = \frac{51000 \cdot 1100}{38000 \cdot 84000}

0.0176rad = \frac{51000N*mm \cdot 1100mm}{38000mm⁴ \cdot 84000N/mm²}

0.0176 = \frac{51000 \cdot 1100}{38000 \cdot 84000}

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Angle of twist of shaft in radians given torque, length of shaft, polar moment of inertia Solution

Follow our step by step solution on how to calculate Angle of twist of shaft in radians given torque, length of shaft, polar moment of inertia?

FIRST Step Consider the formula

θ = \frac{τ \cdot l}{J \cdot C}

Next Step Substitute values of Variables

∴

θ = \frac{51000N*mm \cdot 1100mm}{38000mm⁴ \cdot 84000N/mm²}

Next Step Convert Units

∴

θ = \frac{51N*m \cdot 1.1m}{3.8E-8m⁴ \cdot 8.4E+10Pa}

Next Step Prepare to Evaluate

∴

θ = \frac{51 \cdot 1.1}{3.8E-8 \cdot 8.4E+10}

Next Step Evaluate

∴

θ = 0.0175751879699248rad

LAST Step Rounding Answer

∴

θ = 0.0176rad

Angle of twist of shaft in radians given torque, length of shaft, polar moment of inertia Formula Elements

Variables

Angle of twist of shaft

Angle of twist of shaft is the angle through which the fixed end of a shaft rotates with respect to the free end.

Symbol: θ

Measurement: AngleUnit: rad

Note: Value should be greater than 0.

Formulas to find Angle of twist of shaft

Torsional moment on shaft

Torsional moment on shaft is described as the turning effect of force on the axis of rotation. In brief, it is a moment of force.

Symbol: τ

Measurement: TorqueUnit: N*mm

Note: Value should be greater than 0.

Formulas to find Torsional moment on shaft

Length of Shaft

Length of shaft is defined as the distance between the two opposite ends of a shaft.

Symbol: l

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Length of Shaft

Polar moment of inertia for circular section

Polar moment of inertia for circular section is the measure of the specimen's resistance to torsion.

Symbol: J

Measurement: Second Moment of AreaUnit: mm⁴

Note: Value should be greater than 0.

Formulas to find Polar moment of inertia for circular section

Modulus of Rigidity

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.

Symbol: C

Measurement: StressUnit: N/mm²

Note: Value should be greater than 0.

Formulas to find Modulus of Rigidity

Other formulas in Design of Shaft for Torsional Moment category

Go Torsional shear stress in shaft due to torsional moment

𝜏 = τ \cdot \frac{r}{J}

Go Polar moment of inertia of hollow circular cross-section

J = π \cdot \frac{({d ho}^{4}) - ({d hi}^{4})}{32}

Go Polar moment of inertia of circular cross section

J = π \cdot \frac{{d c}^{4}}{32}

Go Angle of twist of solid cylindrical rod in degrees

𝜽 d = (584 \cdot τ \cdot \frac{l}{C \cdot ({d c}^{4})}) \cdot (\frac{π}{180})

How to Evaluate Angle of twist of shaft in radians given torque, length of shaft, polar moment of inertia?

Angle of twist of shaft in radians given torque, length of shaft, polar moment of inertia evaluator uses Angle of twist of shaft = (Torsional moment on shaft*Length of Shaft)/(Polar moment of inertia for circular section*Modulus of Rigidity) to evaluate the Angle of twist of shaft, Angle of twist of shaft in radians given torque, length of shaft, polar moment of inertia formula is defined as the angle through which the shaft is twisted about its central axis when torque is applied onto it or torsion is acting onto the shaft. Angle of twist of shaft is denoted by θ symbol.

How to evaluate Angle of twist of shaft in radians given torque, length of shaft, polar moment of inertia using this online evaluator? To use this online evaluator for Angle of twist of shaft in radians given torque, length of shaft, polar moment of inertia, enter Torsional moment on shaft (τ), Length of Shaft (l), Polar moment of inertia for circular section (J) & Modulus of Rigidity (C) and hit the calculate button.

FAQs on Angle of twist of shaft in radians given torque, length of shaft, polar moment of inertia

What is the formula to find Angle of twist of shaft in radians given torque, length of shaft, polar moment of inertia?

The formula of Angle of twist of shaft in radians given torque, length of shaft, polar moment of inertia is expressed as Angle of twist of shaft = (Torsional moment on shaft*Length of Shaft)/(Polar moment of inertia for circular section*Modulus of Rigidity). Here is an example- 0.017575 = (51*1.1)/(3.8E-08*84000000000).

How to calculate Angle of twist of shaft in radians given torque, length of shaft, polar moment of inertia?

With Torsional moment on shaft (τ), Length of Shaft (l), Polar moment of inertia for circular section (J) & Modulus of Rigidity (C) we can find Angle of twist of shaft in radians given torque, length of shaft, polar moment of inertia using the formula - Angle of twist of shaft = (Torsional moment on shaft*Length of Shaft)/(Polar moment of inertia for circular section*Modulus of Rigidity).

Can the Angle of twist of shaft in radians given torque, length of shaft, polar moment of inertia be negative?

No, the Angle of twist of shaft in radians given torque, length of shaft, polar moment of inertia, measured in Angle cannot be negative.

Which unit is used to measure Angle of twist of shaft in radians given torque, length of shaft, polar moment of inertia?

Angle of twist of shaft in radians given torque, length of shaft, polar moment of inertia is usually measured using the Radian[rad] for Angle. Degree[rad], Minute[rad], Second[rad] are the few other units in which Angle of twist of shaft in radians given torque, length of shaft, polar moment of inertia can be measured.

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Angle of twist of shaft in radians given torque, length of shaft, polar moment of inertia Formula

Angle of twist of shaft in radians given torque, length of shaft, polar moment of inertia Example

Angle of twist of shaft in radians given torque, length of shaft, polar moment of inertia Solution

Angle of twist of shaft in radians given torque, length of shaft, polar moment of inertia Formula Elements

Other formulas in Design of Shaft for Torsional Moment category

How to Evaluate Angle of twist of shaft in radians given torque, length of shaft, polar moment of inertia?

FAQs on Angle of twist of shaft in radians given torque, length of shaft, polar moment of inertia

Variable Name