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

✖Mass is the quantity of matter in a body regardless of its volume or of any forces acting on it.ⓘ Mass [M]			+10% -10%
✖Base of Triangle is one side in a triangle.ⓘ Base of Triangle [b_tri]			+10% -10%
✖The Height of Triangle is the length of the altitude from the opposite vertex to that base.ⓘ Height of Triangle [H_tri]			+10% -10%

✖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 Moment of Inertia of Triangular Plate about z-axis through Centroid, Perpendicular to Plate [I_zz]

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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)
I_zz = M/72*(3*b_tri^2+4*H_tri^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

I_zz = M/72*(3*b_tri^2+4*H_tri^2) --> 35.45/72*(3*2.82^2+4*2.43^2)

Evaluating ... ...

I_zz = 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)

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Home » Physics » Mechanics » Properties of Planes and Solids » Mechanical » Mass Moment of Inertia » Mass Moment of Inertia of Triangular Plate about z-axis through Centroid, Perpendicular to Plate

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Mass Moment of Inertia of Circular Plate about x-axis Passing through Centroid

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

LaTeX Go

Mass Moment of Inertia about Z-axis = Mass/72*(3*Base of Triangle^2+4*Height of Triangle^2)
I_zz = M/72*(3*b_tri^2+4*H_tri^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 I_zz 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 (b_tri) & Height of Triangle (H_tri) 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 I_zz = M/72*(3*b_tri^2+4*H_tri^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 (b_tri) & Height of Triangle (H_tri). 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 3 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)

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