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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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If angular acceleration is constant, then we can simplify equations of rotational kinematics, similar to the equations of linear kinematics. This simplified set of equations can be used to describe many applications in physics and engineering where the angular acceleration of a system is constant.
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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 torque...
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Radially dependent angular acceleration of twisted light.

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    Scientists demonstrate controlling light

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    Area of Science:

    • Optics and Photonics
    • Quantum Optics

    Background:

    • Structured light allows tailoring of photon properties beyond constant velocity and straight-line propagation.
    • Laguerre-Gaussian modes are essential for carrying orbital angular momentum in twisted light beams.

    Purpose of the Study:

    • To propose and demonstrate a method for controlling the angular acceleration of light.
    • To investigate the complex propagation dynamics of structured light beams through a focus.

    Main Methods:

    • Utilizing superpositions of Laguerre-Gaussian modes with opposite handedness.
    • Theoretical analysis and experimental verification of light beam propagation dynamics.

    Main Results:

    • Radially dependent angular acceleration observed in structured light beams passing through a focus.
    • Complex propagation dynamics due to orbital angular momentum conservation: inner and outer beam parts rotate and accelerate/decelerate oppositely.

    Conclusions:

    • A simple approach to control light's angular acceleration has been developed.
    • Exotic structured light beams exhibit unique behaviors with significant potential in optical trapping, metrology, and fundamental optics research.