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Core - Mechanical Engineering

    Chapter 16

    3-Dimensional Kinetics of a Rigid Body

    16.1 : Moments and Product of Inertia01:23

    16.1 : Moments and Product of Inertia

    The moment of inertia for a differential element of a rigid body can be calculated by multiplying the mass of the element by the square of the shortest ...

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    16.2 : Inertia Tensor01:24

    16.2 : Inertia Tensor

    The inertia tensor is used to describe the distribution of mass and rotational inertia of a rigid body. The inertia tensor is represented using a 3×3 ...

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    16.3 : Moment of Inertia about an Arbitrary Axis01:20

    16.3 : Moment of Inertia about an Arbitrary Axis

    The moment of inertia is typically associated with principal axes, but it can also be computed for any random axis. When an arbitrary axis is under ...

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    16.4 : Angular Momentum about an Arbitrary Axis01:11

    16.4 : Angular Momentum about an Arbitrary Axis

    Consider a rigid body of mass 'm' and a center of mass at point G, rotating in an inertial reference frame. At an arbitrary point P, the angular ...

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    16.5 : Angular Momentum and Principle Axes of Inertia01:09

    16.5 : Angular Momentum and Principle Axes of Inertia

    The angular momentum for a rigid body can be expressed as the integral of the cross-product of the position vector of the mass element with the ...

    198 views
    16.6 : Principle of Impulse and Moment01:15

    16.6 : Principle of Impulse and Moment

    When one considers a rigid body undergoing a plane motion, which is essentially a blend of translational and rotational movement, the application of ...

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    16.7 : Kinetic Energy for a Rigid Body01:13

    16.7 : Kinetic Energy for a Rigid Body

    Consider a rigid body undergoing a general planar motion. Its center of mass is located at point G. The kinetic energy of the i-th particle of the rigid ...

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    16.8 : Equation of Motion for a Rigid Body01:12

    16.8 : Equation of Motion for a Rigid Body

    The motion of a rigid body can be described using equations for translational motion and rotational motion about the center of mass. Newton's Second ...

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    16.9 : Euler Equations of Motion01:19

    16.9 : Euler Equations of Motion

    Consider a rigid body rotating with an angular velocity of ω in an inertial frame of reference. Another rotating frame is attached to the body that ...

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    16.10 : Torque Free Motion01:15

    16.10 : Torque Free Motion

    Torque-free motion refers to the movement of a rigid body without any external torques acting upon it. Consider an axisymmetric object, with the z-axis ...

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