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

Last Updated on February 14, 2024

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

Now, click on Centre of Gravity under Statics

Now, click on Centre of Gravity of a Circular Sector

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).

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.