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Mass Moment of Inertia of Triangular Plate about z-axis through Centroid, Perpendicular to Plate 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}{72} \cdot (3 \cdot {b tri}^{2} + 4 \cdot {H tri}^{2})

I_zz - Mass Moment of Inertia about Z-axis?M - Mass?b_tri - Base of Triangle?H_tri - Height of Triangle?

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

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

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

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

23.3757 = \frac{35.45}{72} \cdot (3 \cdot {2.82}^{2} + 4 \cdot {2.43}^{2})

23.3757kg·m² = \frac{35.45kg}{72} \cdot (3 \cdot {2.82m}^{2} + 4 \cdot {2.43m}^{2})

23.3757 = \frac{35.45}{72} \cdot (3 \cdot {2.82}^{2} + 4 \cdot {2.43}^{2})

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

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

FIRST Step Consider the formula

I zz = \frac{M}{72} \cdot (3 \cdot {b tri}^{2} + 4 \cdot {H tri}^{2})

Next Step Substitute values of Variables

∴

I zz = \frac{35.45kg}{72} \cdot (3 \cdot {2.82m}^{2} + 4 \cdot {2.43m}^{2})

Next Step Prepare to Evaluate

∴

I zz = \frac{35.45}{72} \cdot (3 \cdot {2.82}^{2} + 4 \cdot {2.43}^{2})

Next Step Evaluate

∴

I zz = 23.37573kg·m²

LAST Step Rounding Answer

∴

I zz = 23.3757kg·m²

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

Base of Triangle

Base of Triangle is one side in a triangle.

Symbol: b_tri

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Base of Triangle

Height of Triangle

The Height of Triangle is the length of the altitude from the opposite vertex to that base.

Symbol: H_tri

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Height of Triangle

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 Triangular Plate about z-axis through Centroid, Perpendicular to Plate?

Mass Moment of Inertia of Triangular Plate about z-axis through Centroid, Perpendicular to Plate evaluator uses Mass Moment of Inertia about Z-axis = Mass/72*(3*Base of Triangle^2+4*Height of Triangle^2) to evaluate the Mass Moment of Inertia about Z-axis, The Mass moment of inertia of triangular plate about z-axis through centroid, perpendicular to plate formula is defined as the 1/72 times mass multiplied to sum of three times the square of base of triangle and 4 times the square of height of triangle. Mass Moment of Inertia about Z-axis is denoted by I_zz symbol.

How to evaluate Mass Moment of Inertia of Triangular Plate about z-axis through Centroid, Perpendicular to Plate using this online evaluator? To use this online evaluator for Mass Moment of Inertia of Triangular Plate about z-axis through Centroid, Perpendicular to Plate, enter Mass (M), Base of Triangle (b_tri) & Height of Triangle (H_tri) and hit the calculate button.

FAQs on Mass Moment of Inertia of Triangular Plate about z-axis through Centroid, Perpendicular to Plate

What is the formula to find Mass Moment of Inertia of Triangular Plate about z-axis through Centroid, Perpendicular to Plate?

The formula of Mass Moment of Inertia of Triangular Plate about z-axis through Centroid, Perpendicular to Plate is expressed as Mass Moment of Inertia about Z-axis = Mass/72*(3*Base of Triangle^2+4*Height of Triangle^2). Here is an example- 34.91667 = 35.45/72*(3*2.82^2+4*2.43^2).

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

With Mass (M), Base of Triangle (b_tri) & Height of Triangle (H_tri) we can find Mass Moment of Inertia of Triangular Plate about z-axis through Centroid, Perpendicular to Plate using the formula - Mass Moment of Inertia about Z-axis = Mass/72*(3*Base of Triangle^2+4*Height of Triangle^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 Triangular Plate about z-axis through Centroid, Perpendicular to Plate be negative?

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

Which unit is used to measure Mass Moment of Inertia of Triangular Plate about z-axis through Centroid, Perpendicular to Plate?

Mass Moment of Inertia of Triangular Plate about z-axis through Centroid, Perpendicular to Plate 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 Triangular Plate about z-axis through Centroid, Perpendicular to Plate can be measured.

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