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Related Concept Videos

Torque01:10

Torque

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Torque is an important quantity for describing the dynamics of a rotating rigid body. We see the application of torque in many ways in the world, such as when pressing the accelerator in a car, which causes the engine to apply additional torque on the drivetrain. Here, we define torque and provide a framework to create an equation to calculate torque for a rigid body with fixed-axis rotation.
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Torque Free Motion01:15

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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 observed in environments where there are no external forces or frictions, like in outer space. For example, a rotation of Mars in space is a torque-free motion. Mars is an axisymmetric object, meaning it has an axis of symmetry along which it rotates, designated as the z-axis. The rotating frame of reference is defined such that the center of mass of...
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Net Torque Calculations01:19

Net Torque Calculations

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When a mechanic tries to remove a hex nut with a wrench, it is easier if the force is applied at the farthest end of the wrench handle. The lever arm is the distance from the pivot point (the hex nut in this case) to the person’s hand. If this distance is large, the torque is higher. Only the component of the force perpendicular to the lever arm contributes to the torque. Therefore, pushing the wrench perpendicular to the lever arm is more advantageous. If multiple people apply force to...
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Torque On A Current Loop In A Magnetic Field01:13

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The most common application of magnetic force on current-carrying wires is in electric motors. These consist of loops of wire, which are placed between the magnets with a magnetic field. When current flows through the loops, the magnetic field applies torque, which causes the shaft to rotate, thus converting electrical energy to mechanical energy.
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Physical Principles Governing Gas Exchange01:16

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Gas behavior plays a vital role in understanding bodily processes such as external and internal respiration. External respiration involves the diffusion of oxygen into the blood and carbon dioxide out of it in the lungs. In contrast, internal respiration happens in body tissues, where these gases move in opposite directions.
Gas Laws Governing Respiration
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Correlations02:20

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Correlation means that there is a relationship between two or more variables (such as ice cream consumption and crime), but this relationship does not necessarily imply cause and effect. When two variables are correlated, it simply means that as one variable changes, so does the other. We can measure correlation by calculating a statistic known as a correlation coefficient. A correlation coefficient is a number from -1 to +1 that indicates the strength and direction of the relationship between...
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Magnetic Tweezers for the Measurement of Twist and Torque
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Physical Spin Torques from Exactly Constrained Exchange-Correlation Torques.

Jacques K Desmarais1, Kamel Bencheikh2, Giovanni Vignale3

  • 1Università di Torino, Dipartimento di Chimica, via Giuria 5, 10125 Torino, Italy.

Physical Review Letters
|January 26, 2026
PubMed
Summary
This summary is machine-generated.

This study introduces Spin-current DFT to accurately capture physical spin torques in noncollinear magnetic systems. It resolves spurious exchange-correlation torques, enabling precise spin dynamics simulations.

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Area of Science:

  • Condensed Matter Physics
  • Quantum Mechanics
  • Materials Science

Background:

  • Spin-density functional theory (SDFT) struggles to accurately model physical spin torques in noncollinear magnetic systems.
  • SDFT's limitations include spurious exchange-correlation torques and the inability to rigorously incorporate vector potentials and spin-orbit couplings.

Purpose of the Study:

  • To develop a robust theoretical framework for capturing physical spin torques in noncollinear magnetism.
  • To overcome the limitations of SDFT in describing spin dynamics.

Main Methods:

  • Propose a solution utilizing the U(1)×SU(2) invariance of the exchange-correlation energy within Spin-current DFT.
  • Leverage an exact constraint not accessible to standard SDFT.

Main Results:

  • Achieve nonvanishing exchange-correlation torques on noncollinear solutions that are constrained by internal symmetry.
  • Demonstrate that these constrained torques do not affect spin magnetization propagation.

Conclusions:

  • Spin dynamics are accurately described by physical currents and physical spin torques alone.
  • The proposed Spin-current DFT approach provides a rigorous method for studying spin torques in complex magnetic systems.