How to Calculate the Centre of Gravity of a Circular Sector in Statics | Mechanics

It is possible to calculate the centroid or centre of gravity of a circular sector. There are two highly important parameters one needs to know to compute the centre of gravity of a circular sector. These parameters are:

  • Radius of the Sector (r)
  • Semi Vertical Angle (α)

The formula for computing the centre of gravity of a circular sector is:

C.G. = 2rsinα / 3α

Now, let’s take an example.
Let’s find the centroid or the centre of gravity of a circular sector that has a radius of 4m and a semi vertical angle of 30°.
This implies that:

r = Radius of the Sector = 4
α = Semi Vertical Angle = 30

Entering this values into the formula we have:

C.G. = 2(4)sin30° / 3(30)
C.G. = 8 . sin30° / 90
So, C.G. = 8 . (0.5) / 90
C.G. = 4 / 90
C.G. = 0.0444

Therefore, the centroid or centre of gravity of the circular sector is 0.0444.

How to Calculate the Centre of Gravity of a Circular Sector with Nickzom Calculator

Nickzom Calculator – The Calculator Encyclopedia is capable of calculating the centre of gravity of a circular sector making a semi vertical angle α at a distance from the centre of the sector measured along the central axis.

To get the answer and workings to center of gravity or centroid of a circular sector. First, you need to obtain the Nickzom Calculator – The Calculator Encyclopedia app.

You can get this app via any of these means:

Web – https://www.nickzom.org/calculator-plus
Android (Paid) – https://play.google.com/store/apps/details?id=org.nickzom.nickzomcalculator
Android (Free) – https://play.google.com/store/apps/details?id=com.nickzom.nickzomcalculator
Apple (Paid) – https://itunes.apple.com/us/app/nickzom-calculator/id1331162702?mt=8

Once, you have obtained the calculator encyclopedia app, proceed to the Calculator Map, then click on Mechanics under the Engineering section

How to Calculate the Centre of Gravity of a Circular Sector in Statics | Mechanics

Master Every Calculation Instantly

Unlock solutions for every math, physics, engineering, and chemistry problem with step-by-step clarity. No internet required. Just knowledge at your fingertips, anytime, anywhere.

Now, click on Centre of Gravity under Statics

How to Calculate the Centre of Gravity of a Circular Sector in Statics | Mechanics

Now, click on Centre of Gravity of a Circular Sector

How to Calculate the Centre of Gravity of a Circular Sector in Statics | Mechanics

The screenshot below displays the page or activity to enter your values to get answers for centre of gravity of a circular sector according to the respective parameters which are radius of the sector (r) and semi vertical angle (α).

How to Calculate the Centre of Gravity of a Circular Sector in Statics | Mechanics

Now, enter the values appropriately and accordingly for each of the parameters as required by the example above. A screenshot is below.

Finally, click on Calculate

As you can see from the screenshots above, Nickzom Calculator – The Calculator Encyclopedia solves for the centre of gravity or centroid of a circular sector and presents the formula, workings and steps too.