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

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

GoMass Moment of Inertia of Cuboid about z-axis Passing through Centroid Formula

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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. Check FAQs

I zz = \frac{M}{12} \cdot (3 \cdot {R cyl}^{2} + {H cyl}^{2})

I_zz - Mass Moment of Inertia about Z-axis?M - Mass?R_cyl - Cylinder Radius?H_cyl - Cylinder Height?

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

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Here is how the Mass Moment of Inertia of Solid Cylinder about z-axis through Centroid, Perpendicular to Length equation looks like with Values.

Here is how the Mass Moment of Inertia of Solid Cylinder about z-axis through Centroid, Perpendicular to Length equation looks like with Units.

Here is how the Mass Moment of Inertia of Solid Cylinder about z-axis through Centroid, Perpendicular to Length equation looks like.

11.8585 = \frac{35.45}{12} \cdot (3 \cdot {1.155}^{2} + {0.11}^{2})

11.8585kg·m² = \frac{35.45kg}{12} \cdot (3 \cdot {1.155m}^{2} + {0.11m}^{2})

11.8585 = \frac{35.45}{12} \cdot (3 \cdot {1.155}^{2} + {0.11}^{2})

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

Follow our step by step solution on how to calculate Mass Moment of Inertia of Solid Cylinder about z-axis through Centroid, Perpendicular to Length?

FIRST Step Consider the formula

I zz = \frac{M}{12} \cdot (3 \cdot {R cyl}^{2} + {H cyl}^{2})

Next Step Substitute values of Variables

∴

I zz = \frac{35.45kg}{12} \cdot (3 \cdot {1.155m}^{2} + {0.11m}^{2})

Next Step Prepare to Evaluate

∴

I zz = \frac{35.45}{12} \cdot (3 \cdot {1.155}^{2} + {0.11}^{2})

Next Step Evaluate

∴

I zz = 11.8585419791667kg·m²

LAST Step Rounding Answer

∴

I zz = 11.8585kg·m²

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

Variables

Mass Moment of Inertia about Z-axis

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.

Symbol: I_zz

Measurement: Moment of InertiaUnit: kg·m²

Note: Value can be positive or negative.

Formulas to find Mass Moment of Inertia about Z-axis

Mass

Mass is the quantity of matter in a body regardless of its volume or of any forces acting on it.

Symbol: M

Measurement: WeightUnit: kg

Note: Value can be positive or negative.

Formulas to find Mass

Cylinder Radius

The Cylinder Radius is the radius of its base.

Symbol: R_cyl

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Cylinder Radius

Cylinder Height

Cylinder Height is the shortest distance between the 2 bases of a cylinder.

Symbol: H_cyl

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Cylinder Height

Other Formulas to find Mass Moment of Inertia about Z-axis

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

I zz = \frac{M \cdot r^{2}}{2}

Go Mass Moment of Inertia of Cuboid about z-axis Passing through Centroid

I zz = \frac{M}{12} \cdot (L^{2} + H^{2})

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

I zz = \frac{M}{12} \cdot ({L rect}^{2} + B^{2})

Go Mass Moment of Inertia of Rod about z-axis Passing through Centroid, Perpendicular to Length of Rod

I zz = \frac{M \cdot {L rod}^{2}}{12}

Other formulas in Mass Moment of Inertia category

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

I yy = \frac{M \cdot r^{2}}{4}

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

I xx = \frac{M \cdot r^{2}}{4}

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

I xx = \frac{3}{10} \cdot M \cdot {R c}^{2}

Go Mass Moment of Inertia of Cone about y-axis Perpendicular to Height, Passing through Apex Point

I yy = \frac{3}{20} \cdot M \cdot ({R c}^{2} + 4 \cdot {H c}^{2})

How to Evaluate 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 evaluator uses Mass Moment of Inertia about Z-axis = Mass/12*(3*Cylinder Radius^2+Cylinder Height^2) to evaluate 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 evaluate Mass Moment of Inertia of Solid Cylinder about z-axis through Centroid, Perpendicular to Length using this online evaluator? To use this online evaluator 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.

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

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

The formula of Mass Moment of Inertia of Solid Cylinder about z-axis through Centroid, Perpendicular to Length is expressed as Mass Moment of Inertia about Z-axis = Mass/12*(3*Cylinder Radius^2+Cylinder Height^2). Here is an example- 11.7564 = 35.45/12*(3*1.155^2+0.11^2).

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

With Mass (M), Cylinder Radius (R_cyl) & Cylinder Height (H_cyl) we can find Mass Moment of Inertia of Solid Cylinder about z-axis through Centroid, Perpendicular to Length using the formula - Mass Moment of Inertia about Z-axis = Mass/12*(3*Cylinder Radius^2+Cylinder Height^2).

What are the other ways to Calculate Mass Moment of Inertia about Z-axis?

Here are the different ways to Calculate Mass Moment of Inertia about Z-axis-

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)

Can the Mass Moment of Inertia of Solid Cylinder about z-axis through Centroid, Perpendicular to Length be negative?

Yes, the Mass Moment of Inertia of Solid Cylinder about z-axis through Centroid, Perpendicular to Length, measured in Moment of Inertia can be negative.

Which unit is used to measure 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 is usually measured using the Kilogram Square Meter[kg·m²] for Moment of Inertia. Kilogram Square Centimeter[kg·m²], Kilogram Square Millimeter[kg·m²], Gram Square Centimeter[kg·m²] are the few other units in which Mass Moment of Inertia of Solid Cylinder about z-axis through Centroid, Perpendicular to Length can be measured.

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