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ME 316 Lecture 61 Kinetics (I) 1.Review of Kinetics of Planar Mechanisms - Inertia (mass and moment of inertia) - Governing equation (Newton’s Law) 2. Moment/Product of Inertia – spatial rotation

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ME 316 Lecture 62 Review of Planar Kinetics of a Rigid Body Kinetics : how does a body move under the force or moment ? If there is no any force applied to a body then the body will remain its current status Total resultant force in a direction Motion or no-motion in a specific direction The above is called “Newton First Law”

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ME 316 Lecture 63 Review of Planar Kinetics of a Rigid Body The basic evidence to support the Newton First Law is the inertia 1.A property of an object; 2.A measure of how difficult or easy the motion of a body can be changed; 3. An inherent resistance to change

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ME 316 Lecture 64 Review of Planar Kinetics of a Rigid Body Two types of inertia depending on types of causes Cause is force:inertia is mass (m) Cause is moment:inertia is the moment of inertia (I P ) A B I A ≠ I B

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ME 316 Lecture 65 Review of Planar Kinetics of a Rigid Body I A ≠ I B B A Example (to be filled)

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ME 316 Lecture 66 Review of Planar Kinetics of a Rigid Body B G Parallel – axis theorem (to be filled) G is the center of gravity

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ME 316 Lecture 67 Review of Planar Kinetics of a Rigid Body 1.Translation (T) (to be filled) 2.Rotation (R) (to be filled) 3.General (T + R) (to be filled) Kinetic energy (K)

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ME 316 Lecture 68 Review of Planar Kinetics of a Rigid Body Translation: X and Y axes may not be horizontal or vertical; rather they could be in any direction but not in parallel. Kinetics Equation

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ME 316 Lecture 69 Review of Planar Kinetics of a Rigid Body Rotation: Case 1: P May not be fixed G

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ME 316 Lecture 610 Review of Planar Kinetics of a Rigid Body Case 2:P=G (mass center)

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ME 316 Lecture 611 Review of Planar Kinetics of a Rigid Body Case 3: when P is fixed point

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ME 316 Lecture 612 Translation and rotation Review of Planar Kinetics of a Rigid Body or

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ME 316 Lecture 613 Moment/product of Inertia of Spatial Rotation z

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ME 316 Lecture 614 Product of Inertia Orthogonal planes

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ME 316 Lecture 615 Product of Inertia x

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ME 316 Lecture 616 Product of Inertia If either one or both of the orthogonal planes are planes of symmetry for the mass, the product of inertia with respect to these planes will be zero.

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ME 316 Lecture 617 Moment /Product of Inertia Parallel-axis and parallel-plane theorems

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ME 316 Lecture 618 Moment /Product of Inertia Inertia Tensor – a compact way to express

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ME 316 Lecture 619 Moment /Product of Inertia Principal axes - principal moments of inertia If the coordinate axes are oriented such that two of the three orthogonal planes containing the axes are planes of symmetry for the body, then all the products of inertia for the body are zero with respect to the coordinate planes, and hence the coordinate axes are principal axes of inertia

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ME 316 Lecture 620 Moment /Product of Inertia Moment of inertia about an arbitrary axis

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ME 316 Lecture 621 Moment /Product of Inertia Example 1 Find: the location of center of gravity G and Ix’, Iy’, Iz’ The bent rod ABCD has a weight of 1.5 lb/ft

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ME 316 Lecture 622 Moment /Product of Inertia Example 2 Find: Iz’ of the composite body The 1.5 Kg rod and 4 Kg disk

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ME 316 Lecture 623 Moment /Product of Inertia The bent rod OABC has mass of 4 Kg/m Find: Ix’x’ of the rod Example 3

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