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Related Concept Videos

Equation of Motion for a Rigid Body01:12

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 of the object, point G. This center of mass is the point where the equation of motion for translational motion comes into play, as per Newton's Second Law.
The combined moments generated about the center of mass of the object are equal to the rate of change of the angular momentum of the body. An external force, when applied at a different point...
Planar Rigid-Body Motion01:22

Planar Rigid-Body Motion

Understanding the movement of a rigid body in planar motion involves recognizing that every particle within this body is traversing a path that maintains a consistent distance from a specific plane. This concept is fundamental in the study of physics and mechanical engineering, and it allows us to comprehend better how objects move in space.
Planar motion is typically divided into three distinct categories. The first is rectilinear translation, demonstrated by a subway train that moves along...
Curvilinear Motion: Rectangular Components01:23

Curvilinear Motion: Rectangular Components

Curvilinear motion characterizes the movement of a particle or object along a curved path, notably evident when envisioning a car navigating a winding road. If the car starts at point A, its position vector is established within a fixed frame of reference, where the ratio of the position vector to its magnitude signifies the unit vector pointing in the position vector's direction.
As the car advances, its position evolves over time. Quantifying the car's velocity involves computing the time...
Rigid Body Equilibrium Problems - II01:21

Rigid Body Equilibrium Problems - II

A rigid body is in static equilibrium when the net force and the net torque acting on the system are equal to zero.
Consider two children sitting on a seesaw, which has negligible mass. The first child has a mass (m1) of 26 kg and sits at point A, which is 1.6 meters (r1) from the pivot point B; the second child has a mass (m2) of 32 kg and sits at point C. How far from the pivot point B should the second child sit (r2) to balance the seesaw?
Relative Motion Analysis using Rotating Axes01:25

Relative Motion Analysis using Rotating Axes

Consider a component AB undergoing a linear motion. Along with a linear motion, point B also rotates around point A. To comprehend this complex movement, position vectors for both points A and B are established using a stationary reference frame.
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Rigid Body Equilibrium Problems - I00:49

Rigid Body Equilibrium Problems - I

A rigid body is said to be in static equilibrium when the net force and the net torque acting on the system is equal to zero. To solve for rigid body equilibrium problems, do the following steps.

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Compact Lens-less Digital Holographic Microscope for MEMS Inspection and Characterization
10:28

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Published on: July 5, 2016

Holographic interferometry: compensation for rigid body motion.

C P Hu, J L Turner, C E Taylor

    Applied Optics
    |February 19, 2010
    PubMed
    Summary
    This summary is machine-generated.

    This study introduces a novel optical technique combining holographic interferometry and moiré effect to measure stress. The method generates isopachic fringe patterns unaffected by rigid body motion, accurately reflecting stress changes.

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    Digital Inline Holographic Microscopy (DIHM) of Weakly-scattering Subjects
    10:16

    Digital Inline Holographic Microscopy (DIHM) of Weakly-scattering Subjects

    Published on: February 8, 2014

    Area of Science:

    • Optical Metrology
    • Solid Mechanics
    • Experimental Stress Analysis

    Background:

    • Rigid body motion can contaminate optical stress measurement techniques.
    • Accurate full-field stress analysis is crucial in engineering applications.

    Purpose of the Study:

    • To develop an optical technique for stress analysis that eliminates rigid body motion effects.
    • To provide a full-field isopachic fringe pattern directly related to principal stress sums.

    Main Methods:

    • Combines holographic interferometry with the moiré effect.
    • Utilizes double-exposure holograms recorded from both sides of a model before and after deformation.
    • Superimposes holographic interferometric fringe patterns treated as random grids to generate moiré fringes.

    Main Results:

    • The interference fringe pattern is proportional to the change in model thickness.
    • For plane stress, this is proportional to the sum of principal stresses.
    • The resulting moiré effect is demonstrably free from rigid body motion artifacts.

    Conclusions:

    • The presented technique successfully measures stress distribution independent of rigid body motion.
    • Experimental validation confirms the theoretical predictions.
    • Limitations of the technique are identified and discussed.