Mass Moment of Inertia of Solid Sphere about z-axis Passing through Centroid 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%
✖Radius of Sphere is a line segment extending from the center of a sphere to the circumference or bounding surface.ⓘ Radius of Sphere [R_s]			+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 Sphere about z-axis Passing through Centroid [I_zz]

⎘ Copy

👎

Formula

LaTeX

Reset

👍

Download Properties of Planes and Solids Formulas PDF PDF Image

Mass Moment of Inertia of Solid Sphere about z-axis Passing through Centroid Solution

STEP 0: Pre-Calculation Summary

Formula Used

Mass Moment of Inertia about Z-axis = 2/5*Mass*Radius of Sphere^2
I_zz = 2/5*M*R_s^2
This formula uses 3 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.
Radius of Sphere - (Measured in Meter) - Radius of Sphere is a line segment extending from the center of a sphere to the circumference or bounding surface.

STEP 1: Convert Input(s) to Base Unit

Mass: 35.45 Kilogram --> 35.45 Kilogram No Conversion Required
Radius of Sphere: 0.91 Meter --> 0.91 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

I_zz = 2/5*M*R_s^2 --> 2/5*35.45*0.91^2

Evaluating ... ...

I_zz = 11.742458

STEP 3: Convert Result to Output's Unit

11.742458 Kilogram Square Meter --> No Conversion Required

FINAL ANSWER

11.742458 ≈ 11.74246 Kilogram Square Meter <-- Mass Moment of Inertia about Z-axis

(Calculation completed in 00.004 seconds)

You are here -

Home » Physics » Mechanics » Properties of Planes and Solids » Mechanical » Mass Moment of Inertia » Mass Moment of Inertia of Solid Sphere about z-axis Passing through Centroid

Credits

Created by Chilvera Bhanu Teja

Institute of Aeronautical Engineering (IARE), Hyderabad

Chilvera Bhanu Teja has created this Calculator and 300+ more calculators!

Verified by Vaibhav Malani

National Institute of Technology (NIT), Tiruchirapalli

Vaibhav Malani has verified this Calculator and 200+ more calculators!

< Mass Moment of Inertia Calculators

Mass Moment of Inertia of Cone about x-axis Passing through Centroid, Perpendicular to Base

LaTeX Go Mass Moment of Inertia about X-axis = 3/10*Mass*Radius of Cone^2

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

LaTeX 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

LaTeX 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

LaTeX Go Mass Moment of Inertia about X-axis = (Mass*Radius^2)/4

Mass Moment of Inertia of Solid Sphere about z-axis Passing through Centroid Formula

LaTeX Go

Mass Moment of Inertia about Z-axis = 2/5*Mass*Radius of Sphere^2
I_zz = 2/5*M*R_s^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 Sphere about z-axis Passing through Centroid?

Mass Moment of Inertia of Solid Sphere about z-axis Passing through Centroid calculator uses Mass Moment of Inertia about Z-axis = 2/5*Mass*Radius of Sphere^2 to calculate the Mass Moment of Inertia about Z-axis, The Mass moment of inertia of solid sphere about z-axis passing through centroid formula is defined as the 2/5 times of mass multiplied to square of the radius of sphere. Mass Moment of Inertia about Z-axis is denoted by I_zz symbol.

How to calculate Mass Moment of Inertia of Solid Sphere about z-axis Passing through Centroid using this online calculator? To use this online calculator for Mass Moment of Inertia of Solid Sphere about z-axis Passing through Centroid, enter Mass (M) & Radius of Sphere (R_s) and hit the calculate button. Here is how the Mass Moment of Inertia of Solid Sphere about z-axis Passing through Centroid calculation can be explained with given input values -> 11.74246 = 2/5*35.45*0.91^2.

FAQ

What is Mass Moment of Inertia of Solid Sphere about z-axis Passing through Centroid?

The Mass moment of inertia of solid sphere about z-axis passing through centroid formula is defined as the 2/5 times of mass multiplied to square of the radius of sphere and is represented as I_zz = 2/5*M*R_s^2 or Mass Moment of Inertia about Z-axis = 2/5*Mass*Radius of Sphere^2. Mass is the quantity of matter in a body regardless of its volume or of any forces acting on it & Radius of Sphere is a line segment extending from the center of a sphere to the circumference or bounding surface.

How to calculate Mass Moment of Inertia of Solid Sphere about z-axis Passing through Centroid?

The Mass moment of inertia of solid sphere about z-axis passing through centroid formula is defined as the 2/5 times of mass multiplied to square of the radius of sphere is calculated using Mass Moment of Inertia about Z-axis = 2/5*Mass*Radius of Sphere^2. To calculate Mass Moment of Inertia of Solid Sphere about z-axis Passing through Centroid, you need Mass (M) & Radius of Sphere (R_s). With our tool, you need to enter the respective value for Mass & Radius of Sphere 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 & Radius of Sphere. 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)

Home

FREE PDFs

🔍 Search