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

STEP 0: Pre-Calculation Summary
Formula Used
Angle b/w axis of radius of rotation & line OA = atan(Mass of Ball*Mean Equilibrium Angular Speed^2)
φ = atan(mball*ωequillibrium^2)
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.
Mass of Ball - (Measured in Kilogram) - The mass of ball is the amount of "matter" in the object.
Mean Equilibrium Angular Speed - Mean equilibrium angular speed is the speed of the object in rotational motion.
STEP 1: Convert Input(s) to Base Unit
Mass of Ball: 6 Kilogram --> 6 Kilogram No Conversion Required
Mean Equilibrium Angular Speed: 13 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
φ = atan(mballequillibrium^2) --> atan(6*13^2)
Evaluating ... ...
φ = 1.56981013382073
STEP 3: Convert Result to Output's Unit
1.56981013382073 Radian -->89.9434953048116 Degree (Check conversion here)
FINAL ANSWER
89.9434953048116 89.9435 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 Formula

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

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?

Angle between Axis of Radius of Rotation and Line Joining Point on Curve to Origin calculator uses Angle b/w axis of radius of rotation & line OA = atan(Mass of Ball*Mean Equilibrium Angular Speed^2) to calculate the Angle b/w axis of radius of rotation & line OA, Angle between axis of radius of rotation and line joining point on curve to origin 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 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, enter Mass of Ball (mball) & Mean Equilibrium Angular Speed equillibrium) and hit the calculate button. Here is how the Angle between Axis of Radius of Rotation and Line Joining Point on Curve to Origin calculation can be explained with given input values -> 5153.383 = atan(6*13^2).

FAQ

What is Angle between Axis of Radius of Rotation and Line Joining Point on Curve to Origin?
Angle between axis of radius of rotation and line joining point on curve to origin formula is defined as the angle subtended by the OA line and axis of the radius of rotation and is represented as φ = atan(mballequillibrium^2) or Angle b/w axis of radius of rotation & line OA = atan(Mass of Ball*Mean Equilibrium Angular Speed^2). The mass of ball is the amount of "matter" in the object & Mean equilibrium angular speed is the speed of the object in rotational motion.
How to calculate Angle between Axis of Radius of Rotation and Line Joining Point on Curve to Origin?
Angle between axis of radius of rotation and line joining point on curve to origin 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(Mass of Ball*Mean Equilibrium Angular Speed^2). To calculate Angle between Axis of Radius of Rotation and Line Joining Point on Curve to Origin, you need Mass of Ball (mball) & Mean Equilibrium Angular Speed equillibrium). With our tool, you need to enter the respective value for Mass of Ball & Mean Equilibrium Angular Speed 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 Mass of Ball & Mean Equilibrium Angular Speed. 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(Controlling Force/Radius of Rotation if Governor is in Mid-Position)
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