Moment of inertia given radius of gyration Solution

STEP 0: Pre-Calculation Summary
Formula Used
Rotational Inertia = Area of Cross-Section*Radius of Gyration^2
Ir = A*kG^2
This formula uses 3 Variables
Variables Used
Rotational Inertia - (Measured in Meter⁴) - Rotational Inertia is a physical property of an object that quantifies its resistance to rotational motion about a particular axis.
Area of Cross-Section - (Measured in Square Meter) - The Area of Cross-Section is the enclosed surface area, product of length and breadth.
Radius of Gyration - (Measured in Meter) - The Radius of Gyration or gyradius is defined as the radial distance to a point that would have a moment of inertia the same as the body's actual distribution of mass.
STEP 1: Convert Input(s) to Base Unit
Area of Cross-Section: 50 Square Meter --> 50 Square Meter No Conversion Required
Radius of Gyration: 4.43 Meter --> 4.43 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Ir = A*kG^2 --> 50*4.43^2
Evaluating ... ...
Ir = 981.245
STEP 3: Convert Result to Output's Unit
981.245 Meter⁴ --> No Conversion Required
FINAL ANSWER
981.245 Meter⁴ <-- Rotational Inertia
(Calculation completed in 00.004 seconds)

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14 Mechanics and Statistics of Materials Calculators

Inclination of Resultant of Two Forces Acting on Particle
Go Inclination of Resultant forces = atan((Second Force*sin(Angle))/(First Force+Second Force*cos(Angle)))
Resultant of Two Forces acting on Particle with Angle
Go Parallel Resultant Force = sqrt(First Force^2+2*First Force*Second Force*cos(Angle)+Second Force^2)
Radius of gyration given moment of inertia and area
Go Radius of Gyration = sqrt(Rotational Inertia/Area of Cross-Section)
Resolution of Force with Angle along Horizontal Direction
Go Horizontal Component of Force = Force at Angle*cos(Angle)
Resolution of Force with Angle along Vertical Direction
Go Vertical component of force = Force at Angle*sin(Angle)
Resultant of Two Forces Acting on Particle at 90 Degrees
Go Resultant force = sqrt(First Force^2+Second Force^2)
Moment of Force
Go Moment of force = Force*Perpendicular Distance between Force and Point
Moment of Couple
Go Moment of Couple = Force*Perpendicular Distance between Two Forces
Moment of inertia given radius of gyration
Go Rotational Inertia = Area of Cross-Section*Radius of Gyration^2
Resultant of Two Forces Acting on Particle at 0 Degrees
Go Parallel Resultant Force = First Force+Second Force
Moment of inertia of circle about diametrical axis
Go Rotational Inertia = (pi*Diameter of Circle^4)/64
Resultant of Two like Parallel Forces
Go Parallel Resultant Force = First Force+Second Force
Resultant of Two Unlike Parallel Forces Unequal in Magnitude
Go Resultant force = First Force-Second Force
Resultant of Two Forces Acting on Particle at 180 Degrees
Go Resultant force = First Force-Second Force

Moment of inertia given radius of gyration Formula

Rotational Inertia = Area of Cross-Section*Radius of Gyration^2
Ir = A*kG^2

What is moment of inertia?

Moment of inertia is defined as the quantity expressed by the body resisting angular acceleration which is the sum of the product of the mass of every particle with its square of a distance from the axis of rotation.

How to Calculate Moment of inertia given radius of gyration?

Moment of inertia given radius of gyration calculator uses Rotational Inertia = Area of Cross-Section*Radius of Gyration^2 to calculate the Rotational Inertia, The Moment of inertia given radius of gyration formula is defined as the product of the area of cross-section and the square of the radius of gyration. Rotational Inertia is denoted by Ir symbol.

How to calculate Moment of inertia given radius of gyration using this online calculator? To use this online calculator for Moment of inertia given radius of gyration, enter Area of Cross-Section (A) & Radius of Gyration (kG) and hit the calculate button. Here is how the Moment of inertia given radius of gyration calculation can be explained with given input values -> 981.245 = 50*4.43^2.

FAQ

What is Moment of inertia given radius of gyration?
The Moment of inertia given radius of gyration formula is defined as the product of the area of cross-section and the square of the radius of gyration and is represented as Ir = A*kG^2 or Rotational Inertia = Area of Cross-Section*Radius of Gyration^2. The Area of Cross-Section is the enclosed surface area, product of length and breadth & The Radius of Gyration or gyradius is defined as the radial distance to a point that would have a moment of inertia the same as the body's actual distribution of mass.
How to calculate Moment of inertia given radius of gyration?
The Moment of inertia given radius of gyration formula is defined as the product of the area of cross-section and the square of the radius of gyration is calculated using Rotational Inertia = Area of Cross-Section*Radius of Gyration^2. To calculate Moment of inertia given radius of gyration, you need Area of Cross-Section (A) & Radius of Gyration (kG). With our tool, you need to enter the respective value for Area of Cross-Section & Radius of Gyration 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 Rotational Inertia?
In this formula, Rotational Inertia uses Area of Cross-Section & Radius of Gyration. We can use 1 other way(s) to calculate the same, which is/are as follows -
  • Rotational Inertia = (pi*Diameter of Circle^4)/64
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