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Mass Moment of Inertia of Rod about z-axis Passing through Centroid, Perpendicular to Length of Rod 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 \cdot {L rod}^{2}}{12}

I_zz - Mass Moment of Inertia about Z-axis?M - Mass?L_rod - Length of Rod?

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

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

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

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

11.8167 = \frac{35.45 \cdot 2^{2}}{12}

11.8167kg·m² = \frac{35.45kg \cdot {2m}^{2}}{12}

11.8167 = \frac{35.45 \cdot 2^{2}}{12}

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

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

I zz = \frac{35.45kg \cdot {2m}^{2}}{12}

Next Step Prepare to Evaluate

∴

I zz = \frac{35.45 \cdot 2^{2}}{12}

Next Step Evaluate

∴

I zz = 11.8166666666667kg·m²

LAST Step Rounding Answer

∴

I zz = 11.8167kg·m²

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

Length of Rod

The length of rod is defined as the total length of the conducting rod.

Symbol: L_rod

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Length of Rod

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

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

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 Rod about z-axis Passing through Centroid, Perpendicular to Length of Rod?

Mass Moment of Inertia of Rod about z-axis Passing through Centroid, Perpendicular to Length of Rod evaluator uses Mass Moment of Inertia about Z-axis = (Mass*Length of Rod^2)/12 to evaluate the Mass Moment of Inertia about Z-axis, The Mass moment of inertia of rod about z-axis passing through centroid, perpendicular to length of rod formula is defined as the product of mass and square of length of the rod, divided by 12. Mass Moment of Inertia about Z-axis is denoted by I_zz symbol.

How to evaluate Mass Moment of Inertia of Rod about z-axis Passing through Centroid, Perpendicular to Length of Rod using this online evaluator? To use this online evaluator for Mass Moment of Inertia of Rod about z-axis Passing through Centroid, Perpendicular to Length of Rod, enter Mass (M) & Length of Rod (L_rod) and hit the calculate button.

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

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

The formula of Mass Moment of Inertia of Rod about z-axis Passing through Centroid, Perpendicular to Length of Rod is expressed as Mass Moment of Inertia about Z-axis = (Mass*Length of Rod^2)/12. Here is an example- 11.81667 = (35.45*2^2)/12.

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

With Mass (M) & Length of Rod (L_rod) we can find Mass Moment of Inertia of Rod about z-axis Passing through Centroid, Perpendicular to Length of Rod using the formula - Mass Moment of Inertia about Z-axis = (Mass*Length of Rod^2)/12.

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 Rod about z-axis Passing through Centroid, Perpendicular to Length of Rod be negative?

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

Which unit is used to measure Mass Moment of Inertia of Rod about z-axis Passing through Centroid, Perpendicular to Length of Rod?

Mass Moment of Inertia of Rod about z-axis Passing through Centroid, Perpendicular to Length of Rod 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 Rod about z-axis Passing through Centroid, Perpendicular to Length of Rod can be measured.

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