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Related Concept Videos

Kinematic Equations - I01:26

Kinematic Equations - I

13.2K
When an object moves with constant acceleration, the velocity of the object changes at a constant rate throughout the motion. The kinematic equations of motions are derived for such cases where the acceleration of the object is constant. The first kinematic equation gives an insight into the relationship between velocity, acceleration, and time. We can see, for example:
13.2K
Kinematic Equations - II01:17

Kinematic Equations - II

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The second kinematic equation expresses the final position of an object in terms of its initial position, the distance traveled with the initial constant velocity, and the distance traveled due to a change in velocity. Similar to the first kinematic equation, this equation is also only valid when the acceleration is constant throughout the motion of an object.
Suppose a car merges into freeway traffic on a 200 m long ramp. If its initial velocity is 10 m/s and it accelerates at 2 m/s2, then the...
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Kinematic Equations - III01:18

Kinematic Equations - III

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The first two kinematic equations have time as a variable, but the third kinematic equation is independent of time. This equation expresses final velocity as a function of the acceleration and distance over which it acts. The fourth kinematic equation does not have an acceleration term and provides the final position of the object at time t in terms of the initial and final velocities. This equation is useful when the value of the constant acceleration is unknown.
Using the kinematic equations,...
9.9K
Conservation of Angular Momentum: Application01:18

Conservation of Angular Momentum: Application

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A system's total angular momentum remains constant if the net external torque acting on the system is zero. Examples of such systems include a freely spinning bicycle tire that slows over time due to torque arising from friction, or the slowing of Earth's rotation over millions of years due to frictional forces exerted on tidal deformations. However in the absence of a net external torque, the angular momentum remains conserved. The conservation of angular momentum principle requires a...
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Equation of Rotational Dynamics01:08

Equation of Rotational Dynamics

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Angular variables are introduced in rotational dynamics. Comparing the definitions of angular variables with the definitions of linear kinematic variables, it is seen that there is a mapping of the linear variables to the rotational ones. Linear displacement, velocity, and acceleration have their equivalents in rotational motion, which are angular displacement, angular velocity, and angular acceleration. Similar to the rotational variables, a mapping exists from Newton's second law of motion...
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Kinematic Equations for Rotation01:30

Kinematic Equations for Rotation

1.1K
In mechanics, when one observes a rigid body in rotational motion with constant angular acceleration, it is possible to establish equations for its rotational kinematics. This process resembles how linear kinematics are dealt with in simpler motion studies.
For instance, imagine a point A on a rigid body engaged in circular motion. The translational velocity of this particular point can be calculated by taking the time derivatives of the displacement equation, which essentially measures the...
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Related Experiment Video

Updated: May 2, 2026

Proton Transfer and Protein Conformation Dynamics in Photosensitive Proteins by Time-resolved Step-scan Fourier-transform Infrared Spectroscopy
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Proton Transfer and Protein Conformation Dynamics in Photosensitive Proteins by Time-resolved Step-scan Fourier-transform Infrared Spectroscopy

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Restraining Interproton Angular and Distance Dynamics with KEnRef.

Amr Alhossary1, Colin A Smith1

  • 1Department of Chemistry, Wesleyan University, Middletown, Connecticut 06457, United States.

The Journal of Physical Chemistry. B
|March 9, 2026
PubMed
Summary
This summary is machine-generated.

KEnRef refines protein structures by rigorously accounting for interproton distance and angular fluctuations. This novel approach enables ultraquantitative nuclear magnetic resonance (NMR)-based ensemble refinement, improving structural and dynamic property modeling.

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Related Experiment Videos

Last Updated: May 2, 2026

Proton Transfer and Protein Conformation Dynamics in Photosensitive Proteins by Time-resolved Step-scan Fourier-transform Infrared Spectroscopy
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Study of Protein Dynamics via Neutron Spin Echo Spectroscopy
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Area of Science:

  • Biophysics
  • Computational Biology
  • Structural Biology

Background:

  • Traditional NMR structure determination is limited by complex mathematics and neglects interproton angular motion.
  • Advanced methods like exact NOE (eNOE) and residual dipolar coupling (RDC) lack physical realism due to ignored dynamic effects.

Purpose of the Study:

  • To introduce KEnRef, an open-source C++ library for refining multistate protein structures.
  • To rigorously account for interproton distance and angular fluctuations in structural refinement.
  • To enable ultraquantitative NMR-based ensemble refinement.

Main Methods:

  • Implemented the Kinetic Ensemble approach in KEnRef.
  • Developed a novel loss function with fractional exponents for balanced sensitivity.
  • Integrated KEnRef with GROMACS for molecular dynamics simulations.

Main Results:

  • Achieved ~0.2 Å interproton RMSD and 2 ns convergence time in single-structure simulations.
  • Demonstrated 100-fold restraint energy decreases and highly correlated distance/angular fluctuations (R > 0.85) in two-structure ensembles.
  • Validated KEnRef's capacity to capture localized protein motions and dynamic properties.

Conclusions:

  • KEnRef enables integrated refinement of distance and angular fluctuations for accurate structural and dynamic modeling.
  • The library's performance and modular design support advanced NMR-based ensemble refinement.
  • KEnRef provides a foundation for ultraquantitative analysis of protein dynamics using NMR data.