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Digital simulations are especially helpful in physics education, but most simulations provide only a visual- ization of a phenomenon while obscuring the mathematical relationships that model its behavior. Our team is developing a suite of online simulations called DynamicsLab, which combine visual representations with an ability to input and alter the governing physics equations. Here, we share excerpts from a group of clinical interviews, in which intermediate physics students explored the first iterations of a DynamicsLab simulation of a characteristic problem in Classical Mechanics: the bead on a spinning hoop. The students were given predict- observe-explain prompts to investigate the way they connected the mathematical representation to the physical phenomenon. We highlight three episodes in which students had to revise unsuccessful predictions, and how these instances indicate that engaging with the DynamicsLab simulation encouraged the students to draw upon a more diverse range of knowledge elements to support their physical and mathematical reasoning. 

The ability to measure the charge and size of single particles is essential to understanding particle adhesion and interaction with their environment. Characterizing the physical properties of biological particles, like cells, can be a powerful tool in studying the association between the changes in physical properties and disease development. Currently, measuring charge via the electrophoretic mobility (μep) of individual particles remains challenging, and there is only one prior report of simultaneously measuring μep and size. We introduce microfluidic transverse AC electrophoresis (TrACE), a novel technique that combines particle tracking velocimetry (PTV) and AC electrophoresis. In TrACE, electric waves with 0.75 to 1.5 V amplitude are applied transversely to the bulk flow and cause the particles to oscillate. PTV records the particles' oscillating trajectories as pressure drives bulk flow through the microchannel. A simple quasi-equilibrium model agrees well with experimental measurements of frequency, amplitude, and phase, indicating that particle motion is largely described by DC electrophoresis. The measured μep of polystyrene particles (0.53, 0.84, 1, and 2 μm diameter) are consistent with ELS measurements, and precision is enhanced by averaging ∼100 measurements per particle. Particle size is simultaneously measured from Brownian motion quantified from the trajectory for particles <2 μm or image analysis for particles ≥2 μm. Lastly, the ability to analyze intact mammalian cells is demonstrated with B cells. TrACE systems are expected to be highly suitable as fieldable tools to measure the μep and size of a broad range of individual particles. 

As seen by an observer in the rotating frame, the earth’s small spheroidal deformations neutralize the centrifugal force, leaving only the smaller Coriolis force to govern the “inertial” motion of objects that move on its surface, assumed smooth and frictionless. Previous studies of inertial motion employ weakly spheroidal equations of motion that ignore the influence of the centrifugal force and yet treat the earth as a sphere. The latitude dependence of these equations renders them strongly nonlinear. We derive and justify these equations and use them to identify, classify, name, describe, and illustrate all possible classes of inertial motion, including a new class of motion called circumpolar waves, which encircle both poles during each cycle of the motion. We illustrate these classes using CorioVis, our freely available Coriolis visualization software. We identify a rotational/time-reversal symmetry for motion on the earth’s surface and use this symmetry to develop and validate closed-form small-amplitude approximations for the four main classes and one degenerate class of inertial motion. For these five classes, we supply calculations of experimentally relevant frequencies, zonal drifts, and latitude ranges. 

We analyze the rotational dynamics of six magnetic dipoles of identical strength at the vertices of a regular hexagon with a variable-strength dipole in the center. The seven dipoles spin freely about fixed axes that are perpendicular to the plane of the hexagon, with their dipole moments directed parallel to the plane. Equilibrium dipole orientations are calculated as a function of the relative strength of the central dipole. Small-amplitude perturbations about these equilibrium states are calculated in the absence of friction and are compared with analytical results in the limit of zero and infinite central dipole strength. Normal modes and frequencies are presented. Bifurcations are seen at two critical values of the central dipole strength, with bistability between these values.