Angle between Axis of Radius of Rotation and Line Joining Point on Curve to Origin O Calculator

✖Controlling Force is the inward force acting on the rotating balls is known as controlling force.ⓘ Controlling Force [F_c]			+10% -10%
✖Radius of Rotation if Governor is in Mid-Position is the linear distance from its axis of rotation to a point of interest on the body.ⓘ Radius of Rotation if Governor is in Mid-Position [r_rotation]			+10% -10%

✖Angle b/w axis of radius of rotation & line OA is the angle made by the axis of radius of rotation and line joining a point (A) on the curve to the origin O.ⓘ Angle between Axis of Radius of Rotation and Line Joining Point on Curve to Origin O [φ]

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Formula

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Angle between Axis of Radius of Rotation and Line Joining Point on Curve to Origin O

Formula

`"φ" = atan("F"_{"c"}/"r"_{"rotation"})`

Example

`"41.82017°"=atan("17N"/"19m")`

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Angle between Axis of Radius of Rotation and Line Joining Point on Curve to Origin O Solution

STEP 0: Pre-Calculation Summary

Formula Used

Angle b/w axis of radius of rotation & line OA = atan(Controlling Force/Radius of Rotation if Governor is in Mid-Position)
φ = atan(F_c/r_rotation)
This formula uses 2 Functions, 3 Variables

Functions Used

tan - The tangent of an angle is a trigonometric ratio of the length of the side opposite an angle to the length of the side adjacent to an angle in a right triangle., tan(Angle)
atan - Inverse tan is used to calculate the angle by applying the tangent ratio of the angle, which is the opposite side divided by the adjacent side of the right triangle., atan(Number)

Variables Used

Angle b/w axis of radius of rotation & line OA - (Measured in Radian) - Angle b/w axis of radius of rotation & line OA is the angle made by the axis of radius of rotation and line joining a point (A) on the curve to the origin O.
Controlling Force - (Measured in Newton) - Controlling Force is the inward force acting on the rotating balls is known as controlling force.
Radius of Rotation if Governor is in Mid-Position - (Measured in Meter) - Radius of Rotation if Governor is in Mid-Position is the linear distance from its axis of rotation to a point of interest on the body.

STEP 1: Convert Input(s) to Base Unit

Controlling Force: 17 Newton --> 17 Newton No Conversion Required
Radius of Rotation if Governor is in Mid-Position: 19 Meter --> 19 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

φ = atan(F_c/r_rotation) --> atan(17/19)

Evaluating ... ...

φ = 0.729899658151732

STEP 3: Convert Result to Output's Unit

0.729899658151732 Radian -->41.8201698801436 Degree (Check conversion here)

FINAL ANSWER

41.8201698801436 ≈ 41.82017 Degree <-- Angle b/w axis of radius of rotation & line OA

(Calculation completed in 00.004 seconds)

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< 13 Basics of Governor Calculators

Total Downward Force on Sleeve in Wilson-Hartnell Governor

Go Force = Mass on Sleeve*Acceleration due to Gravity+(Tension in the auxiliary spring*Distance of auxiliary spring from mid of lever)/Distance of main spring from mid point of lever

Speed of Rotation in RPM

Go Mean Equilibrium Speed in RPM = 60/(2*pi)*sqrt((tan(Angle b/w axis of radius of rotation & line OA))/Mass of Ball)

Ratio of Length of Arm to Length of Link

Go Ratio of Length of Link to Length of Arm = tan(Angle of Inclination of Link to Vertical)/tan(Angle of Inclination of Arm to Vertical)

Corresponding Radial Force Required at Each Ball for Spring Loaded Governors

Go Corresponding Radial Force Required at Each Ball = (Force Required at Sleeve to Overcome Friction*Length of sleeve arm of lever)/(2*Length of ball arm of lever)

Angle between Axis of Radius of Rotation and Line Joining Point on Curve to Origin O

Go Angle b/w axis of radius of rotation & line OA = atan(Controlling Force/Radius of Rotation if Governor is in Mid-Position)

Angle between Axis of Radius of Rotation and Line Joining Point on Curve to Origin

Go Angle b/w axis of radius of rotation & line OA = atan(Mass of Ball*Mean Equilibrium Angular Speed^2)

Mean Equilibrium Speed in RPM

Go Mean Equilibrium Speed in RPM = (Minimum equilibrium speed in r.p.m+Maximum equilibrium speed in r.p.m)/2

Mean Equilibrium Angular Speed

Go Mean Equilibrium Angular Speed = (Minimum equilibrium angular speed+Maximum equilibrium angular speed)/2

Sleeve Load for Decrease in Speed Value when Taking Friction into Account

Go Sleeve load for decrease in speed = Total load on sleeve-Force Required at Sleeve to Overcome Friction

Sleeve Load for Increase in Speed Value when Taking Friction into Account

Go Sleeve load for increase in speed = Total load on sleeve+Force Required at Sleeve to Overcome Friction

Increased Speed

Go Increased Speed = Mean Equilibrium Speed in RPM*(1+Percentage Increase in Speed)

Governor Power

Go Power = Mean Effort*Lift of Sleeve

Height of Watt Governor

Go Height of Governor = 895/(Speed in RPM^2)

Angle between Axis of Radius of Rotation and Line Joining Point on Curve to Origin O Formula

Angle b/w axis of radius of rotation & line OA = atan(Controlling Force/Radius of Rotation if Governor is in Mid-Position)
φ = atan(F_c/r_rotation)

What is Porter Governor?

Porter Governor is a modification of Watt Governor with a central load attached to the sleeve. This load moves up and down the central spindle. The additional force increases the speed of revolution required to enable the balls to rise to any predetermined level.

How to Calculate Angle between Axis of Radius of Rotation and Line Joining Point on Curve to Origin O?

Angle between Axis of Radius of Rotation and Line Joining Point on Curve to Origin O calculator uses Angle b/w axis of radius of rotation & line OA = atan(Controlling Force/Radius of Rotation if Governor is in Mid-Position) to calculate the Angle b/w axis of radius of rotation & line OA, The Angle between axis of radius of rotation and line joining point on curve to origin O formula is defined as the angle subtended by the OA line and axis of the radius of rotation. Angle b/w axis of radius of rotation & line OA is denoted by φ symbol.

How to calculate Angle between Axis of Radius of Rotation and Line Joining Point on Curve to Origin O using this online calculator? To use this online calculator for Angle between Axis of Radius of Rotation and Line Joining Point on Curve to Origin O, enter Controlling Force (F_c) & Radius of Rotation if Governor is in Mid-Position (r_rotation) and hit the calculate button. Here is how the Angle between Axis of Radius of Rotation and Line Joining Point on Curve to Origin O calculation can be explained with given input values -> 2396.119 = atan(17/19).

FAQ

What is Angle between Axis of Radius of Rotation and Line Joining Point on Curve to Origin O?

The Angle between axis of radius of rotation and line joining point on curve to origin O formula is defined as the angle subtended by the OA line and axis of the radius of rotation and is represented as φ = atan(F_c/r_rotation) or Angle b/w axis of radius of rotation & line OA = atan(Controlling Force/Radius of Rotation if Governor is in Mid-Position). Controlling Force is the inward force acting on the rotating balls is known as controlling force & Radius of Rotation if Governor is in Mid-Position is the linear distance from its axis of rotation to a point of interest on the body.

How to calculate Angle between Axis of Radius of Rotation and Line Joining Point on Curve to Origin O?

The Angle between axis of radius of rotation and line joining point on curve to origin O formula is defined as the angle subtended by the OA line and axis of the radius of rotation is calculated using Angle b/w axis of radius of rotation & line OA = atan(Controlling Force/Radius of Rotation if Governor is in Mid-Position). To calculate Angle between Axis of Radius of Rotation and Line Joining Point on Curve to Origin O, you need Controlling Force (F_c) & Radius of Rotation if Governor is in Mid-Position (r_rotation). With our tool, you need to enter the respective value for Controlling Force & Radius of Rotation if Governor is in Mid-Position 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 Angle b/w axis of radius of rotation & line OA?

In this formula, Angle b/w axis of radius of rotation & line OA uses Controlling Force & Radius of Rotation if Governor is in Mid-Position. We can use 1 other way(s) to calculate the same, which is/are as follows -

Angle b/w axis of radius of rotation & line OA = atan(Mass of Ball*Mean Equilibrium Angular Speed^2)

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