Angular Velocity of Driving Shaft given Angular Acceleration of Driven Shaft Calculator

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Driveline Angular Velocity

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✖Angular Acceleration of Driven Shaft is the rate of the angular displacement of the driven shaft.ⓘ Angular Acceleration of Driven Shaft [α_B]			+10% -10%
✖Angle Rotated by Driven Shaft is the angular displacement of the driven shaft.ⓘ Angle Rotated by Driven Shaft [Φ]			+10% -10%
✖The Angle between Driving and Driven Shafts is the inclination of the driven shaft with respect to the driving shaft.ⓘ Angle between Driving and Driven Shafts [α]			+10% -10%

✖Angular Velocity of Driven Shaft is the angular displacement of the driven shaft in a given unit of time.ⓘ Angular Velocity of Driving Shaft given Angular Acceleration of Driven Shaft [ω_B]

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Formula

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Angular Velocity of Driving Shaft given Angular Acceleration of Driven Shaft

Formula

`"ω"_{"B"} = sqrt(("α"_{"B"}*(1-cos("Φ")^2*sin("α")^2)^2)/(cos("α")*sin("α")^2*sin(2*"Φ")))`

Example

`"61.99461rad/s"=sqrt(("14.75rad/s²"*(1-cos("15°")^2*sin("5°")^2)^2)/(cos("5°")*sin("5°")^2*sin(2*"15°")))`

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Angular Velocity of Driving Shaft given Angular Acceleration of Driven Shaft Solution

STEP 0: Pre-Calculation Summary

Formula Used

Angular Velocity of Driven Shaft = sqrt((Angular Acceleration of Driven Shaft*(1-cos(Angle Rotated by Driven Shaft)^2*sin(Angle between Driving and Driven Shafts)^2)^2)/(cos(Angle between Driving and Driven Shafts)*sin(Angle between Driving and Driven Shafts)^2*sin(2*Angle Rotated by Driven Shaft)))
ω_B = sqrt((α_B*(1-cos(Φ)^2*sin(α)^2)^2)/(cos(α)*sin(α)^2*sin(2*Φ)))
This formula uses 3 Functions, 4 Variables

Functions Used

sin - Sine is a trigonometric function that describes the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse., sin(Angle)
cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., cos(Angle)
sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)

Variables Used

Angular Velocity of Driven Shaft - (Measured in Radian per Second) - Angular Velocity of Driven Shaft is the angular displacement of the driven shaft in a given unit of time.
Angular Acceleration of Driven Shaft - (Measured in Radian per Square Second) - Angular Acceleration of Driven Shaft is the rate of the angular displacement of the driven shaft.
Angle Rotated by Driven Shaft - (Measured in Radian) - Angle Rotated by Driven Shaft is the angular displacement of the driven shaft.
Angle between Driving and Driven Shafts - (Measured in Radian) - The Angle between Driving and Driven Shafts is the inclination of the driven shaft with respect to the driving shaft.

STEP 1: Convert Input(s) to Base Unit

Angular Acceleration of Driven Shaft: 14.75 Radian per Square Second --> 14.75 Radian per Square Second No Conversion Required
Angle Rotated by Driven Shaft: 15 Degree --> 0.2617993877991 Radian (Check conversion here)
Angle between Driving and Driven Shafts: 5 Degree --> 0.0872664625997001 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

ω_B = sqrt((α_B*(1-cos(Φ)^2*sin(α)^2)^2)/(cos(α)*sin(α)^2*sin(2*Φ))) --> sqrt((14.75*(1-cos(0.2617993877991)^2*sin(0.0872664625997001)^2)^2)/(cos(0.0872664625997001)*sin(0.0872664625997001)^2*sin(2*0.2617993877991)))

Evaluating ... ...

ω_B = 61.9946141270659

STEP 3: Convert Result to Output's Unit

61.9946141270659 Radian per Second --> No Conversion Required

FINAL ANSWER

61.9946141270659 ≈ 61.99461 Radian per Second <-- Angular Velocity of Driven Shaft

(Calculation completed in 00.004 seconds)

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Created by Peri Krishna Karthik

National Institute of Technology Calicut (NIT Calicut), Calicut, Kerala

Peri Krishna Karthik has created this Calculator and 200+ more calculators!

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national institute of technology hamirpur (NITH ), hamirpur , himachal pradesh

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< 3 Driveline Angular Velocity Calculators

Angular Velocity of Driving Shaft given Angular Acceleration of Driven Shaft

Go Angular Velocity of Driven Shaft = sqrt((Angular Acceleration of Driven Shaft*(1-cos(Angle Rotated by Driven Shaft)^2*sin(Angle between Driving and Driven Shafts)^2)^2)/(cos(Angle between Driving and Driven Shafts)*sin(Angle between Driving and Driven Shafts)^2*sin(2*Angle Rotated by Driven Shaft)))

Angular Velocity of Driving Shaft

Go Angular Velocity of Driving Shaft = Angular Velocity of Driven Shaft/(cos(Angle between Driving and Driven Shafts)/(1-(cos(Angle Rotated by Driving Shaft))^2*(sin(Angle between Driving and Driven Shafts))^2))

Angular Velocity of Driven Shaft

Go Angular Velocity of Driven Shaft = (cos(Angle between Driving and Driven Shafts)/(1-(cos(Angle Rotated by Driving Shaft))^2*(sin(Angle between Driving and Driven Shafts))^2))*Angular Velocity of Driving Shaft

Angular Velocity of Driving Shaft given Angular Acceleration of Driven Shaft Formula

Hooke's Joint

A universal joint is a particular type of connection between two shafts. whose axes are inclined to each other. The most simple type of universal joint is the Hooke's joint which is most widely used because of the fact that it is simple and compact in construction and reasonably efficient at small angles of propeller shaft movement up and down, say up to 18 degrees.

How to Calculate Angular Velocity of Driving Shaft given Angular Acceleration of Driven Shaft?

Angular Velocity of Driving Shaft given Angular Acceleration of Driven Shaft calculator uses Angular Velocity of Driven Shaft = sqrt((Angular Acceleration of Driven Shaft*(1-cos(Angle Rotated by Driven Shaft)^2*sin(Angle between Driving and Driven Shafts)^2)^2)/(cos(Angle between Driving and Driven Shafts)*sin(Angle between Driving and Driven Shafts)^2*sin(2*Angle Rotated by Driven Shaft))) to calculate the Angular Velocity of Driven Shaft, The Angular velocity of driving shaft given angular acceleration of driven shaft formula is used to find the angular displacement of the driven shaft in a given unit of time. Angular Velocity of Driven Shaft is denoted by ω_B symbol.

How to calculate Angular Velocity of Driving Shaft given Angular Acceleration of Driven Shaft using this online calculator? To use this online calculator for Angular Velocity of Driving Shaft given Angular Acceleration of Driven Shaft, enter Angular Acceleration of Driven Shaft (α_B), Angle Rotated by Driven Shaft (Φ) & Angle between Driving and Driven Shafts (α) and hit the calculate button. Here is how the Angular Velocity of Driving Shaft given Angular Acceleration of Driven Shaft calculation can be explained with given input values -> 55.91761 = sqrt((14.75*(1-cos(0.2617993877991)^2*sin(0.0872664625997001)^2)^2)/(cos(0.0872664625997001)*sin(0.0872664625997001)^2*sin(2*0.2617993877991))).

FAQ

What is Angular Velocity of Driving Shaft given Angular Acceleration of Driven Shaft?

The Angular velocity of driving shaft given angular acceleration of driven shaft formula is used to find the angular displacement of the driven shaft in a given unit of time and is represented as ω_B = sqrt((α_B*(1-cos(Φ)^2*sin(α)^2)^2)/(cos(α)*sin(α)^2*sin(2*Φ))) or Angular Velocity of Driven Shaft = sqrt((Angular Acceleration of Driven Shaft*(1-cos(Angle Rotated by Driven Shaft)^2*sin(Angle between Driving and Driven Shafts)^2)^2)/(cos(Angle between Driving and Driven Shafts)*sin(Angle between Driving and Driven Shafts)^2*sin(2*Angle Rotated by Driven Shaft))). Angular Acceleration of Driven Shaft is the rate of the angular displacement of the driven shaft, Angle Rotated by Driven Shaft is the angular displacement of the driven shaft & The Angle between Driving and Driven Shafts is the inclination of the driven shaft with respect to the driving shaft.

How to calculate Angular Velocity of Driving Shaft given Angular Acceleration of Driven Shaft?

The Angular velocity of driving shaft given angular acceleration of driven shaft formula is used to find the angular displacement of the driven shaft in a given unit of time is calculated using Angular Velocity of Driven Shaft = sqrt((Angular Acceleration of Driven Shaft*(1-cos(Angle Rotated by Driven Shaft)^2*sin(Angle between Driving and Driven Shafts)^2)^2)/(cos(Angle between Driving and Driven Shafts)*sin(Angle between Driving and Driven Shafts)^2*sin(2*Angle Rotated by Driven Shaft))). To calculate Angular Velocity of Driving Shaft given Angular Acceleration of Driven Shaft, you need Angular Acceleration of Driven Shaft (α_B), Angle Rotated by Driven Shaft (Φ) & Angle between Driving and Driven Shafts (α). With our tool, you need to enter the respective value for Angular Acceleration of Driven Shaft, Angle Rotated by Driven Shaft & Angle between Driving and Driven Shafts 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 Angular Velocity of Driven Shaft?

In this formula, Angular Velocity of Driven Shaft uses Angular Acceleration of Driven Shaft, Angle Rotated by Driven Shaft & Angle between Driving and Driven Shafts. We can use 1 other way(s) to calculate the same, which is/are as follows -

Angular Velocity of Driven Shaft = (cos(Angle between Driving and Driven Shafts)/(1-(cos(Angle Rotated by Driving Shaft))^2*(sin(Angle between Driving and Driven Shafts))^2))*Angular Velocity of Driving Shaft

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