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Lecture (4)

Lecture (4). Previous lesson (1)Definition of moment of inertia. (2)Law of moment of inertia. (3)Math of moment of inertia. Lesson Decleared Polar moment of inertia and Radius of gyration. Learning outcomes

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Lecture (4)

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  1. Lecture (4)

  2. Previous lesson (1)Definition of moment of inertia. (2)Law of moment of inertia. (3)Math of moment of inertia.

  3. Lesson Decleared Polar moment of inertia and Radius of gyration.

  4. Learning outcomes #After finished this lecture students are able to explain polar moment of inertia,radius of gyration,mass radius of gyration,and also area radius of gyration.

  5. Polar Moment of Inertia • The polar moment of inertia is related to an axis which is basically perpendicular to the plane of an area. If all of the area is assumed to comprise infinitely small areas da then the polar moment of inertia is the sum of all of these areas x r2.The polar moment of inertia is given by • J = ∑ x r2 Fig: Polar moment of inertia

  6. Radius of gyration or gyradius is the name of several related measures of the size of an object, a surface, or an ensemble of points. It is calculated as the root mean square distance of the objects' parts from either its center of gravity or a given axis.

  7. Area Radius of Gyration • The Radius of Gyration kx of an Area (A) about an axis (x) is defined as: • equ. (1) kx • equ. (2) • Where Ix is the Moment of Inertia about the axis (x), and A is the area. If no axis is specified the centroidal axis is assumed. • Using the Perpendicular Axis Theorem and equ. (1) from above it can be shown that: • equ. (3)

  8. Mass Radius of Gyration • The Radius of Gyration kxx of a Mass (m) about an axis (x) is defined as: • equ. (4) k • equ. (5) • Where I is the Moment of Inertia about the axis (x), and m is the mass. • If no axis is specified the centroidal axis is assumed.  

  9. Task # What is polar moment of inertia.? #What is Radious of gyration.? #Explain mass radius of gyration. #Explain area radius of gyration.

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