spin

Examples of spin in the following topics:

• Conservation of Angular Momentum

  • An example of conservation of angular momentum is seen in an ice skater executing a spin, as shown in .
  • (Both F and r are small, and so $\vec \tau = \vec r \times \vec F$ is negligibly small. ) Consequently, she can spin for quite some time.
  • She can also increase her rate of spin by pulling in her arms and legs.
  • An ice skater is spinning on the tip of her skate with her arms extended.
  • In the next image, her rate of spin increases greatly when she pulls in her arms, decreasing her moment of inertia.

• Two-Component Forces

  • If the object is not spinning, it will not start to spin.
  • If the object is spinning, it will continue to spin at the same constant angular velocity.

• Gyroscopes

  • A gyroscope is a spinning wheel or disk in which the axle is free to assume any orientation.
  • Mechanically, a gyroscope is a spinning wheel or disk in which the axle is free to assume any orientation.
  • There are two forces acting on a spinning gyroscope.
  • In figure (a), a person holding the spinning bike wheel lifts it with her right hand and pushes down with her left hand in an attempt to rotate the wheel.
  • As seen in figure (a), the forces on a spinning gyroscope are its weight and the supporting force from the stand.

• Ferromagnetism

  • This dipole moment comes from the more fundamental property of the electron—its quantum mechanical spin.
  • The quantum mechanical nature of this spin limits the electron to only two states: with the magnetic field pointing either "up" or "down" (for any choice of up and down).
  • However, in materials with a filled electron shell, the total dipole moment of the electrons is zero, as the spins are in up/down pairs.
  • Only atoms with partially filled shells (i.e., unpaired spins) can have a net magnetic moment.
  • (According to Hund's rules, the first few electrons in a shell tend to have the same spin, thereby increasing the total dipole moment. )

• Matter and Antimatter

  • Antimatter is composed of antiparticles, which have the same mass as particles of ordinary matter but opposite charge and quantum spin.
  • Antimatter is material composed of antiparticles, which have the same mass as particles of ordinary matter but have opposite charge and quantum spin.

• Paramagnetism and Diamagnetism

  • Generally, the permanent moment is caused by the spin of unpaired electrons in atomic or molecular electron orbitals.
  • Unlike ferromagnets, paramagnets do not retain any magnetization in the absence of an externally applied magnetic field, because thermal motion randomizes the spin orientations responsible for magnetism.
  • Some paramagnetic materials retain spin disorder at absolute zero (meaning they are paramagnetic in the ground state).
  • Even in the presence of the field there is only a small induced magnetization because only a small fraction of the spins will be oriented by the field.

• Spin-Orbit Coupling

  • The simplest of these is the spin-order coupling.
  • More important to notice is that the spin-orbit term vanishes as $c\rightarrow \infty$, so it is indeed a relativistic correction.

• Energies of Electron States

  • A second important fact is that because electrons are indistinguishable, the wave function of more than one electron must be antisymmetric with respect to interchange of any two electrons (within the axioms of non-relativistic QM it could have be symmetric, but one can prove in relativistic QM that the wavefunction must be antisymmetric—the spin-statistics theorem).
  • States with the spin of the electrons aligned have lower energies, or states with larger total spin (S) lie lower in energy.
  • Of those states with a given spin, those with the largest value of L tend to lie lower in energy.
  • These two rules order electron configurations (lists of the values of $n$ and $l$ for a set of electrons: e.g., $4p4d$) into terms with equal energies labels by the total orbital and spin angular momentum ($L$ and $S$) e.g., $^3F$.
  • The superscript is the $2S+1$, the multiplicity of the spin states and the letter is the value of $L$ using the rules described earlier.

• Conservation of Energy in Rotational Motion

  • Clearly, the motor had to work to get the stone spinning.
  • The motor works in spinning the grindstone, giving it rotational kinetic energy.

• Relationship Between Torque and Angular Acceleration

  • If a turntable were spinning counter clockwise (when viewed from the top), and you applied your fingers to opposite sides the turntable would begin to slow its spinning.