Mass Moment of Inertia of Solid Cylinder about z-axis through Centroid, Perpendicular to Length 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%
✖The Cylinder Radius is the radius of its base.ⓘ Cylinder Radius [R_cyl]			+10% -10%
✖Cylinder Height is the shortest distance between the 2 bases of a cylinder.ⓘ Cylinder Height [H_cyl]			+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 Solid Cylinder about z-axis through Centroid, Perpendicular to Length [I_zz]

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Mass Moment of Inertia of Solid Cylinder about z-axis through Centroid, Perpendicular to Length Solution

STEP 0: Pre-Calculation Summary

Formula Used

Mass Moment of Inertia about Z-axis = Mass/12*(3*Cylinder Radius^2+Cylinder Height^2)
I_zz = M/12*(3*R_cyl^2+H_cyl^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.
Cylinder Radius - (Measured in Meter) - The Cylinder Radius is the radius of its base.
Cylinder Height - (Measured in Meter) - Cylinder Height is the shortest distance between the 2 bases of a cylinder.

STEP 1: Convert Input(s) to Base Unit

Mass: 35.45 Kilogram --> 35.45 Kilogram No Conversion Required
Cylinder Radius: 1.155 Meter --> 1.155 Meter No Conversion Required
Cylinder Height: 0.11 Meter --> 0.11 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

I_zz = M/12*(3*R_cyl^2+H_cyl^2) --> 35.45/12*(3*1.155^2+0.11^2)

Evaluating ... ...

I_zz = 11.8585419791667

STEP 3: Convert Result to Output's Unit

11.8585419791667 Kilogram Square Meter --> No Conversion Required

FINAL ANSWER

11.8585419791667 ≈ 11.85854 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 Solid Cylinder about z-axis through Centroid, Perpendicular to Length

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Institute of Aeronautical Engineering (IARE), Hyderabad

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Mass Moment of Inertia of Solid Cylinder about z-axis through Centroid, Perpendicular to Length Formula

LaTeX Go

Mass Moment of Inertia about Z-axis = Mass/12*(3*Cylinder Radius^2+Cylinder Height^2)
I_zz = M/12*(3*R_cyl^2+H_cyl^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 Solid Cylinder about z-axis through Centroid, Perpendicular to Length?

Mass Moment of Inertia of Solid Cylinder about z-axis through Centroid, Perpendicular to Length calculator uses Mass Moment of Inertia about Z-axis = Mass/12*(3*Cylinder Radius^2+Cylinder Height^2) to calculate the Mass Moment of Inertia about Z-axis, The Mass moment of inertia of solid cylinder about z-axis through centroid, perpendicular to length formula is defined as 1/12 times mass multiplied to sum of 3 times the square of radius and square of height of cylinder. Mass Moment of Inertia about Z-axis is denoted by I_zz symbol.

How to calculate Mass Moment of Inertia of Solid Cylinder about z-axis through Centroid, Perpendicular to Length using this online calculator? To use this online calculator for Mass Moment of Inertia of Solid Cylinder about z-axis through Centroid, Perpendicular to Length, enter Mass (M), Cylinder Radius (R_cyl) & Cylinder Height (H_cyl) and hit the calculate button. Here is how the Mass Moment of Inertia of Solid Cylinder about z-axis through Centroid, Perpendicular to Length calculation can be explained with given input values -> 11.7564 = 35.45/12*(3*1.155^2+0.11^2).

FAQ

What is Mass Moment of Inertia of Solid Cylinder about z-axis through Centroid, Perpendicular to Length?

The Mass moment of inertia of solid cylinder about z-axis through centroid, perpendicular to length formula is defined as 1/12 times mass multiplied to sum of 3 times the square of radius and square of height of cylinder and is represented as I_zz = M/12*(3*R_cyl^2+H_cyl^2) or Mass Moment of Inertia about Z-axis = Mass/12*(3*Cylinder Radius^2+Cylinder Height^2). Mass is the quantity of matter in a body regardless of its volume or of any forces acting on it, The Cylinder Radius is the radius of its base & Cylinder Height is the shortest distance between the 2 bases of a cylinder.

How to calculate Mass Moment of Inertia of Solid Cylinder about z-axis through Centroid, Perpendicular to Length?

The Mass moment of inertia of solid cylinder about z-axis through centroid, perpendicular to length formula is defined as 1/12 times mass multiplied to sum of 3 times the square of radius and square of height of cylinder is calculated using Mass Moment of Inertia about Z-axis = Mass/12*(3*Cylinder Radius^2+Cylinder Height^2). To calculate Mass Moment of Inertia of Solid Cylinder about z-axis through Centroid, Perpendicular to Length, you need Mass (M), Cylinder Radius (R_cyl) & Cylinder Height (H_cyl). With our tool, you need to enter the respective value for Mass, Cylinder Radius & Cylinder Height 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, Cylinder Radius & Cylinder Height. 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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