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**Mass & Inertia Session 03-06**

Subject : S1014 / MECHANICS of MATERIALS Year : 2008 Mass & Inertia Session 03-06

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Massa & Inertia Bina Nusantara

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What is Mass ? Mass is such a fundamental quantity that it is hard to define in terms of something else. All mechanical quantities can be defined in terms of mass, length, and time. Bina Nusantara

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**The usual symbol for mass is m and its SI unit is the kilogram. **

What is Mass ? The usual symbol for mass is m and its SI unit is the kilogram. While the mass is normally considered to be an unchanging property of an object, at speeds approaching the speed of light one must consider the increase in the relativistic mass. Bina Nusantara

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**What is the deference between Mass vs Weight ?**

…The weight of an object is the force of gravity on the object and may be defined as the mass times the acceleration of gravity, w = mg Since the weight is a force, its SI unit is the newton. Density is mass/volume. ….. Bina Nusantara

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What is Inertia ? Inertia is the resistance an object has to a change in its state of motion. Bina Nusantara

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What is Inertia ? The principle of inertia is one of the fundamental principles of classical physics which are used to describe the motion of matter and how it is affected by applied forces Bina Nusantara

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**It appears in the relationships for the dynamics of rotational motion. **

What is Moment Inertia ? Moment of inertia is the name given to rotational inertia, the rotational analog of mass for linear motion. It appears in the relationships for the dynamics of rotational motion. The moment of inertia must be specified with respect to a chosen axis of rotation. Bina Nusantara

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**What is Moment Inertia ? I = mr2**

For a point mass the moment of inertia is just the mass times the square of perpendicular distance to the rotation axis, I = mr2 That point mass relationship becomes the basis for all other moments of inertia since any object can be built up from a collection of point masses. Bina Nusantara

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What is Moment Inertia ? Moment of inertia is defined with respect to a specific rotation axis. The moment of inertia of a point mass with respect to an axis is defined as the product of the mass times the distance from the axis squared. The moment of inertia of any extended object is built up from that basic definition. The general form of the moment of inertia involves an integral. Bina Nusantara

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What is Moment Inertia ? Bina Nusantara

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**Moment Inertia http://hyperphysics.phy-astr.gsu.edu/hbase/inecon.html**

Bina Nusantara

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SOLID CYLINDER Bina Nusantara

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**SOLID CYLINDER Central Axis moment of inertia: **

The mass element can be expressed in terms Substituting gives a polynomial form integral: Bina Nusantara

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**SOLID CYLINDER Central Diameter**

Now expressing the mass element dm in terms of z, we can integrate over the length of the cylinder. Bina Nusantara

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Hoop About Symmetry Axis Bina Nusantara

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Hoop About Symmetry Axis Bina Nusantara

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**SOLID SPHERE Symmetry Axis**

Bina Nusantara

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**SOLID SPHERE Symmetry Axis**

Bina Nusantara

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ROD ABOUT Center Bina Nusantara

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ROD ABOUT Center Since the total length L has mass M, then M/L is the proportion of mass to length and the mass element can be expressed as shown. Integrating from -L/2 to +L/2 from the center includes the entire rod Bina Nusantara

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Moment of Inertia axis through center axis through end Bina Nusantara

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Moment of Inertia axis through center axis through end Bina Nusantara

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Moment of Inertia thin-walled hollow solid Bina Nusantara

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Moment of Inertia hollow solid Bina Nusantara

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Moment of Inertia thin-walled hollow Bina Nusantara

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What is Gyration ? Radius of gyration is the name of several related measures of the size of an object, a surface, or an ensemble of points. Bina Nusantara

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Radius of Gyration h1 and b1 are constants. b2 depends on h2 It is possible for two EQUAL areas to have equal MOMENT'S OF INERTIA about the same axis while having different dimensions. d is maximized when h2 goes to zero Bina Nusantara

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**Area Radius of Gyration**

The Radius of Gyration of an Area about a given axis is a distance k from the axis. At this distance k an equivalent area is thought of as a line Area parallel to the original axis. The moment of inertia of this Line Area about the original axis is unchanged. Bina Nusantara

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**Area Radius of Gyration**

The Radius of Gyration kx of an Area (A) about an axis (x) is defined as kx Where Ix is the Moment of Inertia about the axis (x), and A is the area Bina Nusantara

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**Mass Radius of Gyration**

The Radius of Gyration of a Mass about a given axis is a distance k from the axis. At this distance k an equivalent mass is thought of as a Point Mass. The moment of inertia of this Point Mass about the original axis is unchanged Bina Nusantara

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**Mass Radius of Gyration**

The Radius of Gyration kxx of a Mass (m) about an axis (x) is defined as: kxx Where I is the Moment of Inertia about the axis (x), and m is the mass. Bina Nusantara

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**Inertia & Radius of Gyration**

Bina Nusantara

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