Arc Length of Cycloid given Perimeter Solution

STEP 0: Pre-Calculation Summary
Formula Used
Arc Length of Cycloid = (8*Perimeter of Cycloid)/(8+(2*pi))
lArc = (8*P)/(8+(2*pi))
This formula uses 1 Constants, 2 Variables
Constants Used
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
Variables Used
Arc Length of Cycloid - (Measured in Meter) - Arc Length of Cycloid is the distance between two points along a section of a curve.
Perimeter of Cycloid - (Measured in Meter) - The Perimeter of Cycloid is the total distance around the edge of the Cycloid.
STEP 1: Convert Input(s) to Base Unit
Perimeter of Cycloid: 70 Meter --> 70 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
lArc = (8*P)/(8+(2*pi)) --> (8*70)/(8+(2*pi))
Evaluating ... ...
lArc = 39.206940745809
STEP 3: Convert Result to Output's Unit
39.206940745809 Meter --> No Conversion Required
FINAL ANSWER
39.206940745809 39.20694 Meter <-- Arc Length of Cycloid
(Calculation completed in 00.004 seconds)

Credits

Created by Mona Gladys
St Joseph's College (SJC), Bengaluru
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5 Arc Length of Cycloid Calculators

Arc Length of Cycloid given Area
Go Arc Length of Cycloid = 8*sqrt(Area of Cycloid/(3*pi))
Arc Length of Cycloid given Perimeter
Go Arc Length of Cycloid = (8*Perimeter of Cycloid)/(8+(2*pi))
Arc Length of Cycloid given Base Length
Go Arc Length of Cycloid = (4*Base Length of Cycloid)/pi
Arc Length of Cycloid
Go Arc Length of Cycloid = 8*Radius of Circle of Cycloid
Arc Length of Cycloid given Height
Go Arc Length of Cycloid = 4*Height of Cycloid

Arc Length of Cycloid given Perimeter Formula

Arc Length of Cycloid = (8*Perimeter of Cycloid)/(8+(2*pi))
lArc = (8*P)/(8+(2*pi))

What is a Cycloid?

In geometry, a Cycloid is the curve traced by a point on a circle as it rolls along a straight line without slipping. A cycloid is a specific form of trochoid and is an example of a roulette, a curve generated by a curve rolling on another curve. The cycloid, with the cusps pointing upward, is the curve of fastest descent under constant gravity (the brachistochrone curve). It is also the form of a curve for which the period of an object in simple harmonic motion (rolling up and down repetitively) along the curve does not depend on the object's starting position (the tautochrone curve).

How to Calculate Arc Length of Cycloid given Perimeter?

Arc Length of Cycloid given Perimeter calculator uses Arc Length of Cycloid = (8*Perimeter of Cycloid)/(8+(2*pi)) to calculate the Arc Length of Cycloid, The Arc Length of Cycloid given Perimeter formula is defined as the distance between two points along a section of a curve, calculated using its perimeter. Arc Length of Cycloid is denoted by lArc symbol.

How to calculate Arc Length of Cycloid given Perimeter using this online calculator? To use this online calculator for Arc Length of Cycloid given Perimeter, enter Perimeter of Cycloid (P) and hit the calculate button. Here is how the Arc Length of Cycloid given Perimeter calculation can be explained with given input values -> 39.20694 = (8*70)/(8+(2*pi)).

FAQ

What is Arc Length of Cycloid given Perimeter?
The Arc Length of Cycloid given Perimeter formula is defined as the distance between two points along a section of a curve, calculated using its perimeter and is represented as lArc = (8*P)/(8+(2*pi)) or Arc Length of Cycloid = (8*Perimeter of Cycloid)/(8+(2*pi)). The Perimeter of Cycloid is the total distance around the edge of the Cycloid.
How to calculate Arc Length of Cycloid given Perimeter?
The Arc Length of Cycloid given Perimeter formula is defined as the distance between two points along a section of a curve, calculated using its perimeter is calculated using Arc Length of Cycloid = (8*Perimeter of Cycloid)/(8+(2*pi)). To calculate Arc Length of Cycloid given Perimeter, you need Perimeter of Cycloid (P). With our tool, you need to enter the respective value for Perimeter of Cycloid 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 Arc Length of Cycloid?
In this formula, Arc Length of Cycloid uses Perimeter of Cycloid. We can use 4 other way(s) to calculate the same, which is/are as follows -
  • Arc Length of Cycloid = 8*Radius of Circle of Cycloid
  • Arc Length of Cycloid = (4*Base Length of Cycloid)/pi
  • Arc Length of Cycloid = 4*Height of Cycloid
  • Arc Length of Cycloid = 8*sqrt(Area of Cycloid/(3*pi))
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