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Angle of Twist: Problem Solving01:13

Angle of Twist: Problem Solving

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An electric motor applies a torque of 700 N·m to an aluminum shaft, triggering a stable rotation. Two pulleys, B and C, are subjected to torques of 300 N·m and 400 N·m, respectively. The modulus of rigidity is provided as 25 GPa. With the knowledge of the length and diameter of each segment, the twist angle between the two pulleys can be computed. First, a section cut is made between pulleys B and C, and the cut cross-section is analyzed using a free-body diagram. Given that the...
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Unsymmetric Bending - Angle of Neutral Axis01:15

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Unsymmetrical bending occurs when a structural member is subjected to bending moments in a plane that does not align with the member's principal axes. This scenario typically arises in beams and other structural components when loads are applied at non-ideal angles, introducing complexities in stress analysis.
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Angle of Twist - Elastic Range01:13

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Consider a cylindrical shaft with a length denoted by L and a consistent cross-sectional radius referred to as r. This shaft undergoes a torque at the free end. The highest shearing strain within the shaft is directly proportional to the twist angle and the radial distance from the shaft axis. When the shaft behaves elastically, this shearing strain can be articulated using variables such as the applied torque, radial distance, the polar moment of inertia, and the modulus of rigidity. By...
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Cyclohexane does not exist in a planar form due to the high angle and torsional strain it would experience in the planar structure. Instead, it adopts non-planar chair and boat conformations.
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Unsymmetrical bending occurs when the bending moment applied to a structural member does not align with its principal axis. This misalignment leads to complex stress distributions and deflection patterns that differ from those in symmetrical bending, and are essential for designing structures to withstand different loading conditions. In unsymmetrical bending, the neutral axis—where stress is zero—does not necessarily align with the geometric axes of the cross-section. The...
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Related Experiment Video

Updated: Aug 11, 2025

Optimized Fabrication Procedure for High-Quality Graphene-based Moiré Superlattice Devices
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Optimized Fabrication Procedure for High-Quality Graphene-based Moiré Superlattice Devices

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Optimal twist angle for a graphene-like bilayer.

August Romeo1, Hans Supèr1,2

  • 1University of Barcelona, Barcelona, Spain.

Journal of Physics. Condensed Matter : an Institute of Physics Journal
|February 6, 2023
PubMed
Summary
This summary is machine-generated.

Researchers re-evaluated the magic angle in twisted bilayer graphene, finding that deviations in layer properties can alter this critical angle. Non-rotational moiré patterns with differing lattice spacings also lead to vanishing Dirac velocity.

Keywords:
Fermi velocitycurvature dependencegraphenemoiré lattice

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Area of Science:

  • Condensed Matter Physics
  • Materials Science
  • Theoretical Physics

Background:

  • The 'magic angle' in twisted bilayer graphene (TBG) is crucial for observing correlated electronic phenomena.
  • The Bistritzer-MacDonald model provides a framework for understanding TBG electronic properties.
  • Deviations from ideal layer properties can significantly impact TBG behavior.

Purpose of the Study:

  • To re-evaluate the optimal angle for Dirac/Fermi velocity nullity in TBG within the Bistritzer-MacDonald framework.
  • To investigate how non-identical layer properties affect the optimal angle and Dirac velocity.
  • To explore alternative moiré configurations that can lead to vanishing Dirac velocity.

Main Methods:

  • Re-evaluation of the Bistritzer-MacDonald model calculations for TBG.
  • Analysis of alterations due to differing layer properties (spacing, hopping amplitudes).
  • Consideration of lattice mismatch without relative rotation to form moiré patterns.

Main Results:

  • The optimal angle is sensitive to variations in layer properties.
  • Moiré patterns formed by lattices with different spacing lengths (without rotation) can also result in a vanishing Dirac velocity.
  • Curvature can cause variations in hopping amplitudes, leading to wider optimal angles in certain regimes.

Conclusions:

  • The 'magic angle' is not a universal constant and depends on specific material parameters.
  • Non-rotational moiré superlattices offer alternative pathways to achieve flat electronic bands.
  • Understanding these variations is key to designing and controlling electronic properties in moiré materials.