Abstract:
Based on relativistic velocity addition and the conservation of momentum and energy, I present derivations of the expressions for the relativistic momentum and kinetic energy, and $E=mc^2$.

Abstract:
Mermin [Am. J. Phys. {\bf 51}, 1130--1131 (1983)] derived the relativistic addition of the parallel components of velocity using the constancy of the speed of light. In this note, the derivation is extended to the perpendicular components of velocity.

Abstract:
We study the transresistivity $\tensor\rho_{21}$ (or equivalently, the drag rate) of two Coulomb-coupled quantum wells in the presence of a perpendicular magnetic field, using semi-classical transport theory. Elementary arguments seem to preclude any possibility of observation of ``Hall drag'' (i.e., a non-zero off-diagonal component in $\tensor\rho_{21}$). We show that these arguments are specious, and in fact Hall drag can be observed at sufficiently high temperatures when the {\sl intra}layer transport time $\tau$ has significant energy-dependence around the Fermi energy $\varepsilon_F$. The ratio of the Hall to longitudinal transresistivities goes as $T^2 B s$, where $T$ is the temperature, $B$ is the magnetic field, and $s = [\partial\tau/ \partial\varepsilon] (\varepsilon_F)$.

Abstract:
We present derivations of the expressions for the spherical volume averages of static electric and magnetic fields that are virtually identical. These derivations utilize the Coulomb and Biot-Savart laws, and make no use of vector calculus identities or potentials.

Abstract:
In a recent papers, Turner and Turner (2010 {\em Am. J. Phys.} {\bf 78} 905-7) and Jensen (2011 {\em Eur. J. Phys.} {\bf 32} 389-397) analysed the motion of asymmetric rolling rigid bodies on a horizontal plane. These papers addressed the common misconception that the instantaneous point of contact of the rolling body with the plane can be used to evaluate the angular momentum $\mathbf L$ and the torque $\boldsymbol\tau$ in the equation of motion $d\mathbf L/dt = \boldsymbol\tau$. To obtain the correct equation of motion, the "phantom torque" or various rules that depend on the motion of the point about which $\mathbf L$ and $\boldsymbol\tau$ are evaluated were discussed. In this paper, I consider asymmetric disks rolling down an inclined plane and describe the most basic way of obtaining the correct equation of motion; that is, to choose the point about which $\mathbf L$ and $\boldsymbol\tau$ are evaluated that is stationary in an inertial frame.

Abstract:
The role of optical-phonons in frictional drag between two adjacent but electrically isolated two-dimensional electron gases is investigated. Since the optical-phonons in III-V materials have a considerably larger coupling to electrons than acoustic phonons (which are the dominant drag mechanism at low T and large separations) it might be expected that the optical phonons will give a large effect high temperatures. The two key differences between optical and acoustic phonon mediated drag are: (1) the optical phonon mediated interlayer interaction is short-ranged due to their negligible group velocity at the Brillouin zone center; and (2) the typical momentum transfer for an optical phonon mediated scattering is relatively large. These considerations make optical phonon mediated drag difficult to see in single subband GaAs systems, but it may be possible to see the effect in double subband GaAs systems or single subband quantum wells in a material with a lower effective mass and lower optical phonon energy such as InSb.

Abstract:
The total linear electromagnetic field momentum $\mathbf P_{\mathrm{em}}$ of a stationary electric dipole $\mathbf p$ in a static magnetic field $\mathbf B$ is considered. The expression $\mathbf P_{\mathrm{em}} = \frac12\mathbf B \times \mathbf p$, which has previously been implied to hold in all static magnetic field situations, is not valid in general. The contribution of the electromagnetic momentum of the fringing fields of the dipole is discussed. It is shown that when either the static magnetic field or the electric dipole moment is changed, the mechanical impulse on the system equals $-\Delta\mathbf P_{\mathrm{em}}$, and hidden momentum does not need to be invoked in order to conserve total momentum.

Abstract:
I investigate the possibility of using Coulomb drag to detect a precursor of the predicted (but as yet not definitively observed) superfluid transition in electron-hole coupled quantum wells. The drag transresisitivity $\rho_{21}$ is shown to be significantly enhanced above the transition temperature $T_c$ and to diverge logarithmically as $T\to T_c^+$, due to electron-hole pairing fluctuations which are somewhat analogous to the Maki-Thompson contribution to conductivity in metals above the superconducting $T_c$. The enhancement in $\rho_{21}$ is estimated to be detectable at temperatures much higher than $T_c$.

Abstract:
Graphene has recently attracted much interest in material field due to its unique two-dimensional structure and outstanding properties. Various preparation methods of graphene are briefly compared. The physical and mechanical properties of graphene are then introduced. Graphene-based composite becomes one of the most important research frontiers in the application of graphene. A comprehensive review is presented to introduce the latest progress of the graphene related composites, including graphene-polymer composites and graphene-based inorganic nanocomposites, especially introducing the fabrication methods and outstanding performances of the bulk metal-matrix/ graphene composites.