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Chapter 16

3-Dimensional Kinetics of a Rigid Body

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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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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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The moment of inertia is commonly discussed in relation to principal axes, but it can also be calculated for any arbitrary axis. When considering an …
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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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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 …
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Consider a rigid body undergoing a general planar motion, a combination of translational and rotational motion. Newton's second law gives the equation …
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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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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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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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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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Single-molecule techniques make it possible to investigate the behavior of individual biological molecules in solution in real time. These techniques …
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Experimental methods are presented for measuring the rotational and translational motion of anisotropic particles in turbulent fluid flows. 3D printing …
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Kinematic analysis is a powerful method for objective assessment of upper extremity movements in a three-dimensional (3D) space. Three-dimensional motion …