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# Chapter 16 3-Dimensional Kinetics of a Rigid Body

## Moments and Product of Inertia

The calculation of the moment of inertia for a differential element within a rigid body involves multiplying the element's mass by the square of…

## Inertia Tensor

The concept of the inertia tensor is employed to depict the mass distribution and rotational inertia of a solid or rigid object. This tensor is…

## 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…

## Angular Momentum about an Arbitrary Axis

Imagine a rigid body with a mass denoted as 'm', which has its center of mass at point G and is rotating around an inertial reference frame.…

## Angular Momentum and Principal Axes of Inertia

The concept of angular momentum for a solid structure is illustrated as the cumulative result of the cross-product of the position vector of the mass…

## 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…

## Kinetic Energy for a Rigid Body

Imagine a solid object involved in a general planar movement, with its center of mass pinpointed at a spot labeled G. The object's kinetic energy…

## Equation of Motion for a Rigid Body

The movement of a rigid object can be understood through the equations that explain both translational and rotational motion about the center of mass…

## Euler Equations of Motion

Imagine a rigid body that is rotating at an angular velocity of ω within an inertial frame of reference. Along with this, picture a second…

## Torque Free Motion

The torque-free motion refers to the movement of a rigid body in space when no external torques are acting upon it. This type of motion can be…

## Kinematic Analysis Using 3D Motion Capture of Drinking Task in People With and Without Upper-extremity Impairments

Kinematic analysis is a powerful method for objective assessment of upper extremity movements in a three-dimensional (3D) space. Three-dimensional…

## Methods for Measuring the Orientation and Rotation Rate of 3D-printed Particles in Turbulence

Experimental methods are presented for measuring the rotational and translational motion of anisotropic particles in turbulent fluid flows. 3D…

## Magnetic Tweezers for the Measurement of Twist and Torque

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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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