Mass Moment of Inertia of Rectangular 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%
✖Length of Rectangular Section is the total distance from one end to other end, length is the longest side of rectangle.ⓘ Length of Rectangular Section [L_rect]			+10% -10%
✖Breadth of Rectangular Section is the shortest length.ⓘ Breadth of Rectangular Section [B]			+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 Rectangular Plate about z-axis through Centroid, Perpendicular to Plate [I_zz]

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Mass Moment of Inertia of Rectangular 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/12*(Length of Rectangular Section^2+Breadth of Rectangular Section^2)
I_zz = M/12*(L_rect^2+B^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.
Length of Rectangular Section - (Measured in Meter) - Length of Rectangular Section is the total distance from one end to other end, length is the longest side of rectangle.
Breadth of Rectangular Section - (Measured in Meter) - Breadth of Rectangular Section is the shortest length.

STEP 1: Convert Input(s) to Base Unit

Mass: 35.45 Kilogram --> 35.45 Kilogram No Conversion Required
Length of Rectangular Section: 2.01 Meter --> 2.01 Meter No Conversion Required
Breadth of Rectangular Section: 1.99 Meter --> 1.99 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

I_zz = M/12*(L_rect^2+B^2) --> 35.45/12*(2.01^2+1.99^2)

Evaluating ... ...

I_zz = 23.6339241666667

STEP 3: Convert Result to Output's Unit

23.6339241666667 Kilogram Square Meter --> No Conversion Required

FINAL ANSWER

23.6339241666667 ≈ 23.63392 Kilogram Square Meter <-- Mass Moment of Inertia about Z-axis

(Calculation completed in 00.006 seconds)

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

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

LaTeX Go

Mass Moment of Inertia about Z-axis = Mass/12*(Length of Rectangular Section^2+Breadth of Rectangular Section^2)
I_zz = M/12*(L_rect^2+B^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 Rectangular Plate about z-axis through Centroid, Perpendicular to Plate?

Mass Moment of Inertia of Rectangular Plate about z-axis through Centroid, Perpendicular to Plate calculator uses Mass Moment of Inertia about Z-axis = Mass/12*(Length of Rectangular Section^2+Breadth of Rectangular Section^2) to calculate the Mass Moment of Inertia about Z-axis, Mass moment of inertia of rectangular plate about z-axis through centroid, perpendicular to plate formula is defined as the 1/12 times of mass multiplied to sum of squares of length and breadth of rectangle. Mass Moment of Inertia about Z-axis is denoted by I_zz symbol.

How to calculate Mass Moment of Inertia of Rectangular Plate about z-axis through Centroid, Perpendicular to Plate using this online calculator? To use this online calculator for Mass Moment of Inertia of Rectangular Plate about z-axis through Centroid, Perpendicular to Plate, enter Mass (M), Length of Rectangular Section (L_rect) & Breadth of Rectangular Section (B) and hit the calculate button. Here is how the Mass Moment of Inertia of Rectangular Plate about z-axis through Centroid, Perpendicular to Plate calculation can be explained with given input values -> 18.34567 = 35.45/12*(2.01^2+1.99^2).

FAQ

What is Mass Moment of Inertia of Rectangular Plate about z-axis through Centroid, Perpendicular to Plate?

Mass moment of inertia of rectangular plate about z-axis through centroid, perpendicular to plate formula is defined as the 1/12 times of mass multiplied to sum of squares of length and breadth of rectangle and is represented as I_zz = M/12*(L_rect^2+B^2) or Mass Moment of Inertia about Z-axis = Mass/12*(Length of Rectangular Section^2+Breadth of Rectangular Section^2). Mass is the quantity of matter in a body regardless of its volume or of any forces acting on it, Length of Rectangular Section is the total distance from one end to other end, length is the longest side of rectangle & Breadth of Rectangular Section is the shortest length.

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

Mass moment of inertia of rectangular plate about z-axis through centroid, perpendicular to plate formula is defined as the 1/12 times of mass multiplied to sum of squares of length and breadth of rectangle is calculated using Mass Moment of Inertia about Z-axis = Mass/12*(Length of Rectangular Section^2+Breadth of Rectangular Section^2). To calculate Mass Moment of Inertia of Rectangular Plate about z-axis through Centroid, Perpendicular to Plate, you need Mass (M), Length of Rectangular Section (L_rect) & Breadth of Rectangular Section (B). With our tool, you need to enter the respective value for Mass, Length of Rectangular Section & Breadth of Rectangular Section 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, Length of Rectangular Section & Breadth of Rectangular Section. 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*Length of Rod^2)/12

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