Extended Masses
Extended Masses - Related Videos
05:18
Quaternary Structure Modeling Through Chemical Cross-Linking Mass Spectrometry: Extending TX-MS Jupyter Reports
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Cited by 2 •
2021
Targeted cross-linking mass spectrometry creates quaternary protein structure models using mass spectrometry data acquired using up to three different acquisition protocols. When executed as a simplified workflow on the Cheetah-MS web server, the results are reported in a Jupyter Notebook. Here, we demonstrate the technical aspects of how the Jupyter Notebook can be extended for a more in-depth analysis.
01:27
Extended Versions of Green’s Theorem
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2026
Green’s Theorem connects the circulation of a vector field around a closed curve with the behavior of the field across the region enclosed by that curve. It provides a way to replace a line integral around a boundary with a double integral over the interior region, making it especially useful in plane geometry, fluid flow, and vector calculus.Although Green’s Theorem is often introduced using simple regions without gaps, it can also be applied to regions made from several simple parts. This...
10:23
Lipid Droplet Isolation for Quantitative Mass Spectrometry Analysis
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Cited by 7 •
2017
Lipid droplets are important organelles for the replication of several pathogens, including the Hepatitis C Virus (HCV). We describe a method to isolate lipid droplets for quantitative mass spectrometry of associated proteins; it can be used under a variety of conditions, such as virus infection, environmental stress, or drug treatment.
01:54
Molar Mass
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2020
The identity of a substance is defined not only by the types of atoms or ions it contains but by the quantity of each type of atom or ion. For example, water, H2O, and hydrogen peroxide, H2O2, are alike in that their respective molecules are composed of hydrogen and oxygen atoms. However, because a hydrogen peroxide molecule contains two oxygen atoms, as opposed to the water molecule, which has only one, the two substances exhibit very different properties. Atoms and molecules are extremely...
01:52
Atomic Mass
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2020
Atoms — and the protons, neutrons, and electrons that compose them — are extremely small. For example, a carbon atom weighs less than 2 × 10−23 g. When describing the properties of tiny objects such as atoms, we use appropriately small units of measure, such as the atomic mass unit (amu). The amu was originally defined based on hydrogen, the lightest element, then later in terms of oxygen. Since 1961, it has been defined with regard to the most abundant isotope of carbon, atoms of which are...
FAQs
Density specifies how mass varies throughout the body and allows each infinitesimal element to be assigned a mass dm. Integrating the contributions from all such elements then produces whole-body quantities. If density is not uniform, regions with different mass content contribute unequally, so the resulting center of mass, inertia, torque, or gravitational field reflects the actual distribution.
The center of mass depends on how mass is distributed, not solely on the body's shape or dimensions. A region containing more mass has greater influence on the integrated position than a lighter region. Consequently, a nonuniform density can shift the center of mass away from the geometric center, affecting how the body is analyzed in mechanical and gravitational problems.
Moment of inertia depends on where the body's mass lies relative to the relevant axis. Mass positioned farther from that axis contributes differently from mass positioned closer to it, so two bodies with the same total mass can have different rotational behavior. Integrating these contributions across the shape captures effects that a point-mass model cannot represent.
A gravitational field produced by an extended body reflects contributions from many mass elements, and those contributions can differ in direction and magnitude across space. Integrating the elements combines their effects into the resulting field. This treatment is important when the body's finite size and shape make a single concentrated mass an inadequate representation of the interaction.
Begin by describing the body's shape and mass distribution with a density function, then divide it conceptually into infinitesimal elements carrying mass dm. Express the desired contribution from each element and integrate over the body's volume. The same workflow can yield the center of mass, moment of inertia, torque, or gravitational field, depending on the quantity being calculated.
An extended-mass model is appropriate when finite size, shape, or internal mass distribution can significantly affect the result. It supports analysis of real bodies in rigid-body motion, rotational dynamics, and gravitational interactions. A point-mass approximation may omit these effects, whereas integration preserves the spatial information needed to obtain more representative mechanical or gravitational quantities.
This approach connects a body's physical distribution to measurable mechanical descriptions, including its center of mass, moment of inertia, torque, and gravitational field. Those results help characterize both translational and rotational behavior and can be applied to orbital interactions. In this way, the method links mathematical integration with models of real objects rather than idealized concentrated masses.