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Angle of Rotation of Arbor with Respect to Drum Formula

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Angle of Rotation of Arbor is defined as how many degrees the arbor is rotated with respect to the drum line. Check FAQs

θ = 12 \cdot M \cdot \frac{l}{E \cdot b \cdot (t^{3})}

θ - Angle of Rotation of Arbor?M - Bending moment in spiral spring?l - Length of Strip of Spiral Spring?E - Modulus of elasticity of spiral spring?b - Width of Strip of Spiral Spring?t - Thickness of Strip of Spring?

Angle of Rotation of Arbor with Respect to Drum Example

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Here is how the Angle of Rotation of Arbor with Respect to Drum equation looks like with Values.

Here is how the Angle of Rotation of Arbor with Respect to Drum equation looks like with Units.

Here is how the Angle of Rotation of Arbor with Respect to Drum equation looks like.

18.4889 = 12 \cdot 1200 \cdot \frac{5980}{207000 \cdot 11.52 \cdot ({1.25}^{3})}

18.4889rad = 12 \cdot 1200N*mm \cdot \frac{5980mm}{207000N/mm² \cdot 11.52mm \cdot ({1.25mm}^{3})}

18.4889 = 12 \cdot 1200 \cdot \frac{5980}{207000 \cdot 11.52 \cdot ({1.25}^{3})}

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Angle of Rotation of Arbor with Respect to Drum Solution

Follow our step by step solution on how to calculate Angle of Rotation of Arbor with Respect to Drum?

FIRST Step Consider the formula

θ = 12 \cdot M \cdot \frac{l}{E \cdot b \cdot (t^{3})}

Next Step Substitute values of Variables

∴

θ = 12 \cdot 1200N*mm \cdot \frac{5980mm}{207000N/mm² \cdot 11.52mm \cdot ({1.25mm}^{3})}

Next Step Convert Units

∴

θ = 12 \cdot 1.2N*m \cdot \frac{5.98m}{2.1E+11Pa \cdot 0.0115m \cdot ({0.0012m}^{3})}

Next Step Prepare to Evaluate

∴

θ = 12 \cdot 1.2 \cdot \frac{5.98}{2.1E+11 \cdot 0.0115 \cdot ({0.0012}^{3})}

Next Step Evaluate

∴

θ = 18.4888888888889rad

LAST Step Rounding Answer

∴

θ = 18.4889rad

Angle of Rotation of Arbor with Respect to Drum Formula Elements

Variables

Angle of Rotation of Arbor

Angle of Rotation of Arbor is defined as how many degrees the arbor is rotated with respect to the drum line.

Symbol: θ

Measurement: AngleUnit: rad

Note: Value should be greater than 0.

Formulas to find Angle of Rotation of Arbor

Bending moment in spiral spring

Bending moment in spiral spring is the reaction induced in a spiral spring when an external force or moment is applied to the element, causing the element to bend.

Symbol: M

Measurement: TorqueUnit: N*mm

Note: Value should be greater than 0.

Formulas to find Bending moment in spiral spring

Length of Strip of Spiral Spring

Length of Strip of Spiral Spring is defined as the length of the thin strip of which spiral spring coils are manufactured.

Symbol: l

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Length of Strip of Spiral Spring

Modulus of elasticity of spiral spring

Modulus of elasticity of spiral spring is a quantity that measures the spring's resistance to being deformed elastically when stress is applied to it.

Symbol: E

Measurement: PressureUnit: N/mm²

Note: Value should be greater than 0.

Formulas to find Modulus of elasticity of spiral spring

Width of Strip of Spiral Spring

The Width of Strip of Spiral Spring is defined as the thickness of the wired strip measured in the lateral direction and by which the spiral spring is manufactured.

Symbol: b

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Width of Strip of Spiral Spring

Thickness of Strip of Spring

The Thickness of Strip of Spring is defined as the thickness of the wired strip by which the spiral spring is manufactured.

Symbol: t

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Thickness of Strip of Spring

Other formulas in Spring Material Mechanics category

Go Maximum Bending Stress induced at outer end of Spring

σ b = 12 \cdot \frac{M}{b \cdot t^{2}}

Go Length of Strip from Outer end to inner End given Angle of Rotation of Arbor

l = θ \cdot E \cdot b \cdot \frac{t^{3}}{12 \cdot M}

Go Modulus of Elasticity given Angle of Rotation of Arbor

E = 12 \cdot M \cdot \frac{l}{θ \cdot b \cdot (t^{3})}

Go Force given Bending Moment Due to that Force

P = \frac{M}{r}

How to Evaluate Angle of Rotation of Arbor with Respect to Drum?

Angle of Rotation of Arbor with Respect to Drum evaluator uses Angle of Rotation of Arbor = 12*Bending moment in spiral spring*Length of Strip of Spiral Spring/(Modulus of elasticity of spiral spring*Width of Strip of Spiral Spring*(Thickness of Strip of Spring^3)) to evaluate the Angle of Rotation of Arbor, Angle of Rotation of Arbor with Respect to Drum formula is defined as a measure of the rotational movement of the arbor in relation to the drum in spiral springs, which is critical in determining the spring's mechanical properties and behavior under various loads. Angle of Rotation of Arbor is denoted by θ symbol.

How to evaluate Angle of Rotation of Arbor with Respect to Drum using this online evaluator? To use this online evaluator for Angle of Rotation of Arbor with Respect to Drum, enter Bending moment in spiral spring (M), Length of Strip of Spiral Spring (l), Modulus of elasticity of spiral spring (E), Width of Strip of Spiral Spring (b) & Thickness of Strip of Spring (t) and hit the calculate button.

FAQs on Angle of Rotation of Arbor with Respect to Drum

What is the formula to find Angle of Rotation of Arbor with Respect to Drum?

The formula of Angle of Rotation of Arbor with Respect to Drum is expressed as Angle of Rotation of Arbor = 12*Bending moment in spiral spring*Length of Strip of Spiral Spring/(Modulus of elasticity of spiral spring*Width of Strip of Spiral Spring*(Thickness of Strip of Spring^3)). Here is an example- 18.48889 = 12*1.2*5.98/(207000000000*0.01152*(0.00125^3)).

How to calculate Angle of Rotation of Arbor with Respect to Drum?

With Bending moment in spiral spring (M), Length of Strip of Spiral Spring (l), Modulus of elasticity of spiral spring (E), Width of Strip of Spiral Spring (b) & Thickness of Strip of Spring (t) we can find Angle of Rotation of Arbor with Respect to Drum using the formula - Angle of Rotation of Arbor = 12*Bending moment in spiral spring*Length of Strip of Spiral Spring/(Modulus of elasticity of spiral spring*Width of Strip of Spiral Spring*(Thickness of Strip of Spring^3)).

Can the Angle of Rotation of Arbor with Respect to Drum be negative?

No, the Angle of Rotation of Arbor with Respect to Drum, measured in Angle cannot be negative.

Which unit is used to measure Angle of Rotation of Arbor with Respect to Drum?

Angle of Rotation of Arbor with Respect to Drum is usually measured using the Radian[rad] for Angle. Degree[rad], Minute[rad], Second[rad] are the few other units in which Angle of Rotation of Arbor with Respect to Drum can be measured.

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Angle of Rotation of Arbor with Respect to Drum Formula

Angle of Rotation of Arbor with Respect to Drum Example

Angle of Rotation of Arbor with Respect to Drum Solution

Angle of Rotation of Arbor with Respect to Drum Formula Elements

Other formulas in Spring Material Mechanics category

How to Evaluate Angle of Rotation of Arbor with Respect to Drum?

FAQs on Angle of Rotation of Arbor with Respect to Drum

Variable Name