Mass Moment of Inertia of Triangular Plate about z-axis through Centroid, Perpendicular to Plate Solution

STEP 0: Pre-Calculation Summary
Formula Used
Mass Moment of Inertia about Z-axis = Mass/72*(3*Base of Triangle^2+4*Height of Triangle^2)
Izz = M/72*(3*btri^2+4*Htri^2)
This formula uses 4 Variables
Variables Used
Mass Moment of Inertia about Z-axis - (Measured in Kilogram Square Meter) - Mass Moment of Inertia about Z-axis of a rigid body is a quantity that determines the torque needed for a desired angular acceleration about a rotational axis.
Mass - (Measured in Kilogram) - Mass is the quantity of matter in a body regardless of its volume or of any forces acting on it.
Base of Triangle - (Measured in Meter) - Base of Triangle is one side in a triangle.
Height of Triangle - (Measured in Meter) - The Height of Triangle is the length of the altitude from the opposite vertex to that base.
STEP 1: Convert Input(s) to Base Unit
Mass: 35.45 Kilogram --> 35.45 Kilogram No Conversion Required
Base of Triangle: 2.82 Meter --> 2.82 Meter No Conversion Required
Height of Triangle: 2.43 Meter --> 2.43 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Izz = M/72*(3*btri^2+4*Htri^2) --> 35.45/72*(3*2.82^2+4*2.43^2)
Evaluating ... ...
Izz = 23.37573
STEP 3: Convert Result to Output's Unit
23.37573 Kilogram Square Meter --> No Conversion Required
FINAL ANSWER
23.37573 Kilogram Square Meter <-- Mass Moment of Inertia about Z-axis
(Calculation completed in 00.004 seconds)

Credits

Created by Chilvera Bhanu Teja
Institute of Aeronautical Engineering (IARE), Hyderabad
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National Institute of Technology (NIT), Tiruchirapalli
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22 Mass Moment of Inertia Calculators

Mass Moment of Inertia of Rectangular Plate about z-axis through Centroid, Perpendicular to Plate
Go Mass Moment of Inertia about Z-axis = Mass/12*(Length of Rectangular Section^2+Breadth of Rectangular Section^2)
Mass Moment of Inertia of Triangular Plate about z-axis through Centroid, Perpendicular to Plate
Go Mass Moment of Inertia about Z-axis = Mass/72*(3*Base of Triangle^2+4*Height of Triangle^2)
Mass Moment of Inertia of Cone about y-axis Perpendicular to Height, Passing through Apex Point
Go Mass Moment of Inertia about Y-axis = 3/20*Mass*(Radius of Cone^2+4*Height of Cone^2)
Mass Moment of Inertia of Solid Cylinder about x-axis through Centroid, Perpendicular to Length
Go Mass Moment of Inertia about X-axis = Mass/12*(3*Cylinder Radius^2+Cylinder Height^2)
Mass Moment of Inertia of Solid Cylinder about z-axis through Centroid, Perpendicular to Length
Go Mass Moment of Inertia about Z-axis = Mass/12*(3*Cylinder Radius^2+Cylinder Height^2)
Mass Moment of Inertia of Cuboid about z-axis Passing through Centroid
Go Mass Moment of Inertia about Z-axis = Mass/12*(Length^2+Height^2)
Mass Moment of Inertia of Cuboid about x-axis Passing through Centroid, Parallel to Length
Go Mass Moment of Inertia about X-axis = Mass/12*(Width^2+Height^2)
Mass Moment of Inertia of Cuboid about y-axis Passing through Centroid
Go Mass Moment of Inertia about Y-axis = Mass/12*(Length^2+Width^2)
Mass Moment of Inertia of Rectangular Plate about x-axis through Centroid, Parallel to Length
Go Mass Moment of Inertia about X-axis = (Mass*Breadth of Rectangular Section^2)/12
Mass Moment of Inertia of Rectangular Plate about y-axis through Centroid, Parallel to Breadth
Go Mass Moment of Inertia about Y-axis = (Mass*Length of Rectangular Section^2)/12
Mass Moment of Inertia of Triangular Plate about x-axis Passing through Centroid, Parallel to Base
Go Mass Moment of Inertia about X-axis = (Mass*Height of Triangle^2)/18
Mass Moment of Inertia of Triangular Plate about y-axis Passing through Centroid, Parallel to Height
Go Mass Moment of Inertia about Y-axis = (Mass*Base of Triangle^2)/24
Mass Moment of Inertia of Solid Sphere about x-axis Passing through Centroid
Go Mass Moment of Inertia about X-axis = 2/5*Mass*Radius of Sphere^2
Mass Moment of Inertia of Solid Sphere about y-axis Passing through Centroid
Go Mass Moment of Inertia about Y-axis = 2/5*Mass*Radius of Sphere^2
Mass Moment of Inertia of Solid Sphere about z-axis Passing through Centroid
Go Mass Moment of Inertia about Z-axis = 2/5*Mass*Radius of Sphere^2
Mass Moment of Inertia of Cone about x-axis Passing through Centroid, Perpendicular to Base
Go Mass Moment of Inertia about X-axis = 3/10*Mass*Radius of Cone^2
Mass Moment of Inertia of Solid Cylinder about y-axis through Centroid, Parallel to Length
Go Mass Moment of Inertia about Y-axis = (Mass*Cylinder Radius^2)/2
Mass Moment of Inertia of Rod about y-axis Passing through Centroid, Perpendicular to Length of Rod
Go Mass Moment of Inertia about Y-axis = (Mass*Length of Rod^2)/12
Mass Moment of Inertia of Rod about z-axis Passing through Centroid, Perpendicular to Length of Rod
Go Mass Moment of Inertia about Z-axis = (Mass*Length of Rod^2)/12
Mass Moment of Inertia of Circular Plate about z-axis through Centroid, Perpendicular to Plate
Go Mass Moment of Inertia about Z-axis = (Mass*Radius^2)/2
Mass Moment of Inertia of Circular Plate about y-axis Passing through Centroid
Go Mass Moment of Inertia about Y-axis = (Mass*Radius^2)/4
Mass Moment of Inertia of Circular Plate about x-axis Passing through Centroid
Go Mass Moment of Inertia about X-axis = (Mass*Radius^2)/4

Mass Moment of Inertia of Triangular Plate about z-axis through Centroid, Perpendicular to Plate Formula

Mass Moment of Inertia about Z-axis = Mass/72*(3*Base of Triangle^2+4*Height of Triangle^2)
Izz = M/72*(3*btri^2+4*Htri^2)

What is mass moment of inertia?

Mass moment of inertia of a body measures the ability of body to resist changes in rotational speed about a specific axis. The larger the Mass Moment of Inertia the smaller the angular acceleration about that axis for a given torque. It basically characterizes the acceleration undergone by an object or solid when torque is applied.

How to Calculate Mass Moment of Inertia of Triangular Plate about z-axis through Centroid, Perpendicular to Plate?

Mass Moment of Inertia of Triangular Plate about z-axis through Centroid, Perpendicular to Plate calculator uses Mass Moment of Inertia about Z-axis = Mass/72*(3*Base of Triangle^2+4*Height of Triangle^2) to calculate the Mass Moment of Inertia about Z-axis, The Mass moment of inertia of triangular plate about z-axis through centroid, perpendicular to plate formula is defined as the 1/72 times mass multiplied to sum of three times the square of base of triangle and 4 times the square of height of triangle. Mass Moment of Inertia about Z-axis is denoted by Izz symbol.

How to calculate Mass Moment of Inertia of Triangular Plate about z-axis through Centroid, Perpendicular to Plate using this online calculator? To use this online calculator for Mass Moment of Inertia of Triangular Plate about z-axis through Centroid, Perpendicular to Plate, enter Mass (M), Base of Triangle (btri) & Height of Triangle (Htri) and hit the calculate button. Here is how the Mass Moment of Inertia of Triangular Plate about z-axis through Centroid, Perpendicular to Plate calculation can be explained with given input values -> 34.91667 = 35.45/72*(3*2.82^2+4*2.43^2).

FAQ

What is Mass Moment of Inertia of Triangular Plate about z-axis through Centroid, Perpendicular to Plate?
The Mass moment of inertia of triangular plate about z-axis through centroid, perpendicular to plate formula is defined as the 1/72 times mass multiplied to sum of three times the square of base of triangle and 4 times the square of height of triangle and is represented as Izz = M/72*(3*btri^2+4*Htri^2) or Mass Moment of Inertia about Z-axis = Mass/72*(3*Base of Triangle^2+4*Height of Triangle^2). Mass is the quantity of matter in a body regardless of its volume or of any forces acting on it, Base of Triangle is one side in a triangle & The Height of Triangle is the length of the altitude from the opposite vertex to that base.
How to calculate Mass Moment of Inertia of Triangular Plate about z-axis through Centroid, Perpendicular to Plate?
The Mass moment of inertia of triangular plate about z-axis through centroid, perpendicular to plate formula is defined as the 1/72 times mass multiplied to sum of three times the square of base of triangle and 4 times the square of height of triangle is calculated using Mass Moment of Inertia about Z-axis = Mass/72*(3*Base of Triangle^2+4*Height of Triangle^2). To calculate Mass Moment of Inertia of Triangular Plate about z-axis through Centroid, Perpendicular to Plate, you need Mass (M), Base of Triangle (btri) & Height of Triangle (Htri). With our tool, you need to enter the respective value for Mass, Base of Triangle & Height of Triangle 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 Mass Moment of Inertia about Z-axis?
In this formula, Mass Moment of Inertia about Z-axis uses Mass, Base of Triangle & Height of Triangle. We can use 6 other way(s) to calculate the same, which is/are as follows -
  • Mass Moment of Inertia about Z-axis = (Mass*Radius^2)/2
  • Mass Moment of Inertia about Z-axis = Mass/12*(Length^2+Height^2)
  • Mass Moment of Inertia about Z-axis = Mass/12*(Length of Rectangular Section^2+Breadth of Rectangular Section^2)
  • Mass Moment of Inertia about Z-axis = (Mass*Length of Rod^2)/12
  • Mass Moment of Inertia about Z-axis = Mass/12*(3*Cylinder Radius^2+Cylinder Height^2)
  • Mass Moment of Inertia about Z-axis = 2/5*Mass*Radius of Sphere^2
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