Welcome back! This week, we’re taking a look at one of demonstrations of simple machines: the pulley, featured in demonstration B3-12.

A pulley is simply a wheel and axle with a rope over it. A system like you see in the picture here, with one or more pulleys in a fixed frame used for exerting tension forces to lift or pull something, is commonly called a block and tackle. The purpose of such a system is to provide mechanical advantage, a multiplication of force, in lifting or pulling a weight.

In this case, we can use the pulleys to lift weight. The energy used to lift the weight against gravity is constant, regardless of how many pulleys are used. But by using the block and tackle, the multiple strands of rope are pulling at the same time – the energy is the same, but the force is multiplied, while we pull more rope through the system.

The pulley-rope-mass system in the image below is in equilibrium, even though there is twice as much mass hanging on one side than on the other – in fact, precisely because there is! The block and tackle in this case doubles the force of the smaller mass, so it holds the larger mass in equilibrium. If we added an extra force by pulling down on the smaller mass, it would move twice as far down as the larger mass moved up.

You can experiment with this at home with this pulley simulation at the Compass Project. Drag the handle in the diagram to apply a force to the system, and see how the mass moves. You can change the number and position of the pulleys, their diameter, and the mass to see how different systems react to different conditions.

The most popular design of telescopes for astronomical research is the reflecting telescope. First developed in the 17^th century, the typical reflecting telescope uses a curved primary mirror to focus incoming light, and a secondary mirror to direct that light to an eyepiece or sensor. There are many variations on the design, but the underlying principle is the same: light is focused largely by reflection, rather than refraction as in a lens-based Galilean refracting telescope, which allows them to avoid both the chromatic aberration common to lenses and the weight required to create very large ones. Reflecting telescopes have a long history in astronomy and astrophysics, from William and Caroline Herschel to the Hubble Space Telescope and beyond.

We have two models in our collection of how reflecting telescopes work. Demonstration L7-14 models the behaviour of light in a reflecting telescope on our optical board, which uses real optical elements to create a viewable two-dimensional ray diagram.

We also have a static model, demonstration E2-54, which shows the construction of a typical reflecting telescope with strings to represent the paths of light rays through the device. The two are best used in combination to show students how this system lets us observe distant objects.

You can experiment with this at home as well, with this simulation from JavaLab. You can adjust the angle of the incoming light and see how it reflects off the primary mirror and forms an image at the secondary mirror, and use an eyepiece lens to focus it on an observer. Try it out at https://javalab.org/en/newtonian_reflector_en/

Welcome back! This week, we’re taking a lot a three different demonstrations that are very valuable for introducing students to optical refraction. Refraction is the process by which light bends as it passes from one medium to another. Consider demonstration L4-03, with a metal rod sitting in a small tank of water; depending on the angle you view it from, the rod may seem to bend or break at the surface; there may even appear to be more than one of it, if you look in through the corner of the tank! And in demonstration L4-06, you can see a laser beam enter a similarly-sized tank of water, changing direction as it passes through the water’s surface.

The degree to which light bends depends on the difference in the index of refraction of each medium, which relates to the relative speeds of wave transmission in the medium. Prisms, lenses, and many other optical devices rely on carefully chosen angles and indices of refraction to create optical effects.

This public domain animation from Wikipedia does an excellent job of illustrating the effect. As the waves pass from one medium to another, the change in propagation speed induces a change in angle, as seen here.

 You can see this happening on a larger scale in demonstration L4-01. Three rays of light are directed through a heavy slab of transparent plastic. The index of refraction of the plastic is much greater than that of air, so the light bends. In the photo below, you can see the beams change direction as they enter and exit the slab.

You can try it for yourself at home with this simulation in the PhET Interactive Simulations Collection: https://phet.colorado.edu/sims/html/bending-light/latest/bending-light_en.html

Today we’re looking at two demonstrations that are often used, individually or together, to discuss simple harmonic motion. Demonstration G1-11: Comparison of Simple Harmonic Motion and Uniform Circular Motion, is a simple mechanical model with a large rotating arm with a disc mounted on it. As the arm-mounted disc rotates around the center, we can see that its motion describes a circle in space. The arm is linked mechanically to a second disc mounted above, that slides back and forth as the arm rotates. The upper disc keeps pace with the lower disc, and as the arm rotates, the upper disc moves back and forth as though it were mounted on a spring.

Demonstration G1-12: Pendulum and Rotating Ball, lets us see that this is not just a coincidence of the model. A ball is mounted as the bob on a rigid pendulum, while an identical ball is mounted on a rotating platform below. The rotating platform is motorized so that it will spin at a constant speed; the pendulum is of an appropriate length so that the period of the swing is the same as the rotational period of the platform. If you start them moving from the same point at the same time, then you can see that the two balls move in sync. By positioning a bright light in front of the apparatus we can project the shadows of both balls on the wall behind, and we can see that the two balls are executing nearly the same motion.

A ball executing simple harmonic motion – the motion of a pendulum bob – is equivalent to the projection of a ball executing uniform circular motion. This is not just a coincidence of the apparatus, but a fundamental discovery about the mathematics behind repeating motion.

(diagram based on public domain work by Wikimedia user Yohai)

 If we make a graph of the linear position of a point on the rotating disc as a function of time, that graph traces out a repeating curve – a curve we can describe with the cosine function, Acos(ɷt),where A is the radius from the center of the circle to the point andt is time. For those of you who have studied thebehaviour of harmonic oscillators, that function should look familiar – it’s the same way we describe an object oscillating without damping, what’s called simple harmonic motion.ɷ(omega) isthe rate of rotation of the disc, and equivalent tothe angular frequency of the oscillation. And conversely, if you made a graph of the velocity of an oscillating mass against its position,rather than plotting the position or the velocity against time,that graph would also trace out a circle. It’s not just a coincidence, but reality – rotational motion and oscillating motion are fundamentally the same phenomenon from a mathematical perspective, just looked at in different dimensions.

 (PD Animation credits: Wikimedia users Chetvorno & Mazemaster)

Let's try this at home. This simulator, by Andrew Duffy of Boston University, lets us model this behaviour on the screen, and see what happens when we change parameters of the motion. Check it out at http://physics.bu.edu/~duffy/HTML5/SHM_circular_motion.html .

 This simulator lets us view this motion in real time. Press Play and see a point rotating on the disc, while two more masses oscillate on springs vertically and horizontally next to the disc. The graph plots out the vertical motion of both the point on the disc and the vertical oscillator over time. You can click the checkbox at the bottom of the screen to form virtual lines between the masses, to show they’re in sync.

Now try changing the experiment. There are two sliders at the bottom of the simulation. The slider on your left lets you change ɷ –try speeding it up and watch what happens! The slider on your right lets you change the radius of the disc, and thus the amplitude of the oscillation.

 Try it out for yourself! And think about where else you’ve seen graphs like that. There are many other physical phenomena that obey similar mathematics, including all types of waves. What examples can you think of?

An important concept in physics is simple harmonic motion – the periodic motion of a mass with a restoring force proportinal to its displacement. This force might come from gravity, a spring, or many other sources, but the same mathematics describes their motion. We have many demonstrations of simple harmonic motion (or SHM) in our collection, including G1-01 and G1-52, which you can see in action in this video starring UMD PhD student Subhayan Sayu.

You can experiment with this at home! Any mass on a spring or on a string or rolling in a well can be a pendulum. Or, try out these Periodic Motion simulations at the PhET Collection: Pendulum Lab or Masses and Springs.

The University of Cambridge offers an example of a simple pendulum experiment to try at home; check it out at https://nrich.maths.org/5376

Welcome back! This week we’re taking a look at demonstration K1-03, which shows the effect of the force that acts on an electrical current in a magnetic field.

A stiffened wire is suspended between the poles of a strong magnet. When we turn on a current through the wire, the wire leaps outwards. If we swap which end of the wire connects to which end of the battery, the direction the wire moves is reversed. What just happened?

The force in play here is known as the Lorentz Force, named for Dutch physicist Hendrik Lorentz, who formalized the equations for this force based on earlier work by James Clerk Maxwell, Oliver Heaviside, and many other scientists. Today Lorentz is most popularly associated with his later work on relativity, supporting the work of Albert Einstein; but this work partly grew out of his early studies of how charged particles interact with electric and magnetic forces.

Lorentz’s equation states (in part) that if an electrically charged particle is moving through a magnetic field, that particle experiences a force proportional to its velocity and to the strength of the magnetic field, but perpendicular to both. So as the electrons flow through the wire, passing through the field of the horseshoe magnet, the resulting force will push the electrons (and thus the wire carrying them) sideways, out from between the poles. If we change the direction of the electrons’ velocity, by swapping the direction of the current, then the direction of the force is reversed; the same happens if we reverse the direction of the magnetic field, by flipping over the magnet.

You can see this in action in an animated simulation from the National High Magnetic Field Laboratory, here: https://nationalmaglab.org/education/magnet-academy/watch-play/interactive/lorentz-force

Click on the switch graphic to complete the circuit, and you can see the motion of the wire. Buttons will let you change the direction of the magnetic field and the current; try one, then the other, then both, and see if what happens matches what you expect!

We’re paying a second visit to the Tesla Coil today, exploring more about how it works. 

Broadly speaking, we can wave our hands at the Tesla Coil and talk about inductance and resonance, but what does that really mean, and how does it lead to those lovely purple sparks?

 Electromagnetic induction is the process by which a voltage is produced across an inductor in a changing magnetic field. In this case, we’re taking advantage of the studies of Maxwell and Faraday that showed the relationship between electricity and magnetism. An electrical current generates its own magnetic field; a changing electrical current thus produces a changing magnetic field, and so a changing electrical current in one conductor can induce a current in a nearby conductor. We can carefully choose these to create higher or lower induced voltages.

Electrical resonance occurs when a circuit is built to have a particular resonant frequency, at which the impedance (the way a circuit element resists an alternating current) of different components cancels out to let the circuit build up higher voltages or currents.

Our Tesla coil, circuit above, uses a 5000 volt transformer to charge a large oil capacitor. When the potential across the capacitor reaches the breakdown potential of the spark gap, breakdown across the gap occurs. The spark gap then becomes a conducting part of the RLC circuit, which resonates at a frequency of about 200 kilohertz. The large coil in the resonant circuit is the primary coil of the final transformer and the long coil of very fine wire is the secondary, producing about 200,000 volts at 200 kilohertz.

You can see what’s happening by examining a simulation of a similar circuit’s behaviour, like https://www.falstad.com/circuit/e-tesla.html . The initial transformer creates a high voltage, which eventually builds up enough to exceed the breakdown voltage of the air and make a spark across the spark gap. This then feeds into resonant circuits which build up very high electrical potential, which can create the discharge we see.

This uses Paul Falstad’s Circuit Simulator Applet, which you can explore further at https://www.falstad.com/circuit/index.html

To learn more about Tesla Coils, check out:

Nikola Tesla’s patent: https://patents.google.com/patent/US1119732

Richie Burnett’s Operation of the Tesla Coil: http://www.richieburnett.co.uk/operation.html

Wikipedia: https://en.wikipedia.org/wiki/Tesla_coil

Kelley and Dunbar, “The Tesla Coil,” American Journal of Physics 20(32). https://doi.org/10.1119/1.1933098

A recurring favourite optics demonstration in many of our classes is N1-05 Spectra: Visible and Invisible. This seemingly simple setup can show us some important truths about electromagnetic radiation.

A carbon arc lamp is used to create a bright, broad-spectrum white light. This is an example of what is known (confusingly) as blackbody radiation, the light that an object emits due to its temperature. Technically, a hot object radiates light across many frequencies, but what we think of as its “color” is made up of the frequency ranges with the greatest intensity, which depends on the object’s temperature. This we see here a bright blue-white light, with high emission across all the visible frequencies.

 Lenses right next to the source focus this light onto a narrow slit, which then passes a narrow beam of light, focused by an additional lens, to a prism. The prism refracts the light at different angles depending on its frequency. So projected onto the wall we will see, rather than a spot of bright white light, a spectrum of all the colors making up the light.

 But here’s what’s interesting about this carbon arc lamp. Not all of the light is in that visible range! We have a fluorescent screen, which glows in the visible light range when it absorbs higher-frequency ultraviolet light; using this, we can see that there are bright bands of ultraviolet light off beyond the blue end of the visible spectrum on the wall.

 So does this mean there’s something off beyond the red end as well? To check this, we have a thermopile, a horn containing a series of sensors that sense when they get warm. Using this, connected to an audio oscillator that changes pitch when the thermopile senses heat, we can scan across the wall… and indeed, we can hear the pitch change when the horn is in the dark area past the red end of the spectrum. There is infrared light hiding here, frequencies too low for us to see!

 To learn more about light spectra, check out this simulation from the University of Colorado’s PhET Collection: Blackbody Radiation  https://phet.colorado.edu/en/simulation/blackbody-spectrum

You can vary the temperature of your source and see how that changes not only the intensity of light, but its color – or, more accurately, its distribution of color. A light source can radiate light across a broad range of frequencies, which may be centered within, above, or below the range we can see. Try it out for yourself, compare the spectra of a household lightbulb to the Sun or another star, and see if you can guess the temperature of the arc lamp we use here!

This week we’re taking a look at two related demonstrations of Lenz’s Law, K2-42 and K2-43.

We’ve seen before in our blog that a moving conductor in a magnetic field generates eddy currents, and that these eddy currents have their own magnetic fields that can interact with the original magnet.

Lenz’s Law formulates this more precisely: that if a conductor has an electrical current induced in it by a magnetic field, that current will be in a direction such that the magnetic field it creates opposes changes in the initial magnetic field.

Heinrich Emil Lenz was a 19^th century physicist who spent much of his career teaching at the University of St Petersburg in Russia. Prior to this, he spent several years doing research at sea, studying meteorology and the properties of seawater. He is best remembered today, though, for his work on electromagnetism, including his law of electromagnetic forces published in 1834.

This is what allows things like magnetic braking, as discussed in the blog post linked above, to work – the continued movement of the conductor will change the magnetic field passing through it, so the induced current opposes this motion, slowing the swing of the pendulum. We can see this illustrated more clearly in a few more demonstrations.

Demonstration K2-43 has some simple conducting coils, one copper and one aluminum, hanging from strings. When you push a horseshoe magnet through the coils, the coil is dragged along with the magnet, as the magnetic field from the induced current is resisting the change in the field – and thus the coil moves to keep up! Conversely, in demonstration K2-42, if you drop a magnet through a conducting tube, it slows down as it falls, the eddy currents creating a magnetic field that drag back the falling magnet. You can try it out at home with a magnet and a loop of wire. Just be sure the loop forms a complete circuit; as you can see in K2-43, an incomplete loop won’t produce much current!

Or if you don’t have a magnet handy, try out this simple simulation from Michael Davidson of Florida State. As you move the bar magnet on the screen, you can see the current start to flow, and the magnetic field lines of the current appear next to the field lines of the bar magnet. When the magnet is stationary, there is no change in the magnetic field, and so no current is produced until you move it again.

 Originally appearing in our demonstration catalog as J3-23 and now as the updated K8-46, the Faraday Cage and Radio Waves demonstration is a popular way of showing how a conductive surface interferes with the passage of electric fields, and thus can prevent the transmission of electromagnetic waves.

Now, our own Don Lynch has created an animation of the physics behind this demonstration; check it out below! 

 The Lecture-Demonstration Facility is introducing a series of teaching aid animations of popular demonstrations; watch for more coming soon!

The Van de Graaff Generator is our most popular way of demonstrating electrostatic phenomena in the classroom. Don Lynch has created a new animation to help illustrate how this beloved device works.

The Van de Graaff generator uses essentially similar triboelectric phenomena to the classic charging by friction demonstrations we often use at the beginning of any class on electricity, and that you have probably performed by accident on dry winter days in carpeted rooms. A grounded comb at the bottom exchanges charges with the moving belt, then this surplus of charge is deposited through the upper comb on the large conductive dome. The individual identical charges repel each other, so they become distributed across the entire outer surface of the dome.

 You can find this animation, along with a growing collection of others, on our Teaching Aids page!

(And always remember: It’s Van de Graaff, with two F’s. With one F, it’s the band. Don’t mix them up!)

We love our demonstrations, but there are some things you can’t easily demonstrate in the classroom, either because the physics isn’t compatible with that environment, or because the scale is beyond what we can practically see. This is where simulations can be valuable, in letting us go beyond what we can do on the tabletop and look inside the black boxes. 

The quantum nature of the hydrogen atom is a good example. We can demonstrate the emission spectrum of hydrogen with the Balmer Series demonstration P3-51, and we have simple models of electron orbitals for more complex atoms, but how can we look at the structure of the hydrogen atom itself?

Here are some simulations available for looking inside our smallest atom.

• Falstad offers this illustration of the energy levels of the hydrogen atoms, which allows you to switch the view between the Bohr and Dirac models within a single active diagram https://www.falstad.com/nw/hydrogen.html

• The PhET model hydrogen atom lets you compare different historical models of the atom to simulated experimental results https://phet.colorado.edu/sims/cheerpj/hydrogen-atom/latest/hydrogen-atom.html?simulation=hydrogen-atom

• Andrew Duffy’s Emission Spectra simulator lets you compare the hydrogen spectrum with other visible spectra side-by-side with the full white light spectrum, for orientation http://physics.bu.edu/~duffy/HTML5/emission_spectra.html

• This more complex Falstad simulator lets you display the wave functions/orbitals in either real or complex modes, and to take slices along the axes as well as viewing them in three dimensions. This is potentially valuable for upper level courses analyzing the orbital structure. http://www.falstad.com/qmatom/

It’s a hectic time for teaching, and our circumstances change every day. Fortunately, there are resources out there to help with making an online class engaging and informative.

UMD’s Keep Teaching #4Maryland site offers links to university resources for instructors, including ELMS tips, Labster simulated experiments, and library resources. Check it out at https://svp.umd.edu/keepteaching.

UMD IT also offers a catalog of resources for teaching and learning; check it out here!

Here at the Physics Lecture-Demonstration Facility, we’re compiling additional resources to help with remote and distanced learning.

• We have begun creating animated Teaching Aids to help explicate popular demonstrations and other important aspects of physics; as we post them you can find them linked on the individual demonstration pages and on the Teaching Aids gallery page.

• We are compiling a Directory of Simulations from elsewhere on the web as well, with tested simulations for many categories of physics, including some very difficult to demonstrate in the classroom. Check them out here!

• And don’t forget to explore this very blog for Demonstration Highlights that may include videos, simulations, and at-home activities; and News Tips with recent events in science. Every blog post also has topical tags to link you to other related articles in the blog.

• UPDATE 10/1/2020: Be sure to check out our new Demonstration Videos channel!

Some additional articles and websites with tips:

• Claire Major: Teaching Online: a guide to theory, research, and practice. Ebook available through the UMD Libraries

• Richard Byrne: “How to Increase the Chances of Your Students Actually Watching Your Instructional Videos”

• Bethany Wilcox & Michael Vignal: “Recommendations for emergency remote teaching based on the student experience”

• Argenta Price, Carl Wieman, & Katherine Perkins: “Teaching With Simulations”

• Maryland Open Source Textbook Commons

• AAPT: Resources for College and University Physics Faculty

• The AAPT ComPADRE Digital Library

• National Science Digital Library

• Science in School: "Keeping science engaging: Online resources for students during COVID-19"

Just a quick newstip today to call your attention to a few recent papers in science education and science information that might be of interest.

• Teaching with simulations to help improve student engagement:

Price, A., Wieman, C., & Perkins, K. (2020). Teachers use simulations for student motivation, content learning, and engagement in science practices. National Science Teaching Association: Teaching with Simulations 

• A recent article in Quantitative Science Studies looks at the real-world policy impact of studies of the scientific process and science communication:

Hicks, D., & Isett, K. R. (2020). Powerful numbers: Exemplary quantitative studies of science that had policy impact. Quantitative Science Studies, 1(3), 969-982. https://doi.org/10.1162/qss_a_00060

• A look at how students learn to understand graphs, and to use graphs to understand scientific concepts:

Boda, P., Bathia, S., & Linn, M. (2020). Longitudinal impact of interactive science activities: Developing, implementing, and validating a graphing integration inventory. Journal of Research in Science Teaching, https://doi.org/10.1002/tea.21653

• Forming and testing hypotheses in the classroom helps college students’ motivation in science classes, helps them learn to feel like a scientist, and ultimately helps them learn:

Starr., C. et al. (2020). Engaging in science practices in classrooms predicts increases in undergraduates' STEM motivation, identity, and achievement: A short‐term longitudinal study. Journal of Research in Science Teaching, 57(7), 1093-1118. https://doi.org/10.1002/tea.21623

Three recent articles related to science education may be of interest to our readers.

• The first, an article in The Physics Teacher by Andrew G. Duffy of Boston University, introduces his collection of new simulations for use in teaching physics. Many of these have been indexed in our own Directory of Simulations as well, and it is very much worth checking out his collection site https://tinyurl.com/HTML5sims and given the article a read to learn more about their development. https://aapt.scitation.org/doi/full/10.1119/10.0006921

•  The next article, in Physics Today, is a collaboration by Brad Conrad of SPS, AIP research fellow Rachel Ivie, and Patrick Mulvey and Starr Nicholson of AIP’s Statistical Research Center. They explore the latest results on how COVID-19 has impacted undergraduate physics students, and steps we can take to support them. They note that the impact has been greatest on already underrepresented groups. https://physicstoday.scitation.org/do/10.1063/PT.6.5.20211102a/full/

• The third, an article in Science in School by Ed Walsh of Collins Learning in the UK, explores the art and science of demonstrations and their use in the classroom. https://www.scienceinschool.org/article/2021/art-science-demonstration/

NASA’s Eyes is a newly updated visualization app available for computers and some mobile devices that lets users explore NASA science data as a multimedia experience.

 Developed by The NASA/Caltech Jet Propulsion Laboratory, Eyes offers three main portals: Eyes on the Earth, featuring Earth sensing and climate information; Eyes on the Solar System, with information on the planets and NASA exploration missions, and Eyes on Exoplanets, exploring the worlds beyond.

 In Eyes on the Earth, users are initially treated to an overview of tracks of Earth-sensing stellites, plus a popup window with the latest relevant news stories. Clicking on a satellite tells you more abouts its mission; clicking on a new story zooms in on the relevant part of the earth, with satellite imagery and a summary of the news. A menu bar along the top lets you select other data – the latest visual mosaic image of Earth from space, current surface temperatures, CO & CO2 emissions, recent sea level variation, soil moisture, gravitational field variations, salinity, and many others.

 Eyes on the Solar System similarly opens with a zoomable view of the Solar System, showing the orbits and current positions of the planets and the tracks of current space probes. Any of these can be clicked on to zoom in for further imagery and data. Once zoomed in on a planet, moons are presented the same way, and can be selected and zoomed in on in turn.

 Eyes on Exoplanets is available both in the app and as a mobile-friendly website. Presenting a broad overview of the galaxy, you can zoom in on telescope images of the areas around currently known exoplanets and access data and imagery.

• Check it out at https://eyes.nasa.gov/
•  FAQ: https://eyes.nasa.gov/faq.html
• Accessibility: https://eyes.nasa.gov/accessibility.html
• News & Updates: https://twitter.com/nasa_eyes

‘Tis the spooky season, and what could be more seasonal than bats? This week we’re exploring a different kind of bats than the usual, though. So let’s take a swing at the physics of baseball and softball bats!

A baseball or softball bat is an irregularly shaped object that is swung as a lever and then experiences a large impact. This impact sets up vibrations in the bat; you can see several vibrational modes modeled on this webpage created by Dan Russell of Penn State University: https://www.acs.psu.edu/drussell/Demos/batvibes.html He illustrates here that wooden bats are solid, and bend lengthwise, like a tuning bar; aluminum and composite bats, however, are frequently hollow, and can flex across their diameters as well, like a hoop or bell.

One of the most widely recognized specialists in the field of baseball physics is Alan Nathan of the University of Illinois; you can check out his homepage here: http://baseball.physics.illinois.edu/ where he discusses many aspects of the physics of the sport, current and historical. Particularly interesting is his collection of slow-motion images of ball and bat collisions and their analysis: http://baseball.physics.illinois.edu/ball-bat.html .

 You can experiment with this physics yourself with our demonstration D2-21 Center of Percussion: Bat and Mallet. 

 Many articles have been published over the years exploring the physics of bats, particularly with a view to classroom discussion. We’ve collected for you some highlights from the American Journal of Physics and The Physics Teacher, presented chronologically so you can explore the development of this topic over time.

H. Brody. “The sweet spot of a baseball bat”

American Journal of Physics 54, 640 (1986); https://doi.org/10.1119/1.14854

Explores the idea of a bat’s “sweet spot,” the point of impact at which maximum energy is imparted to the ball.

G. Watts & S. Baroni. “Baseball–bat collisions and the resulting trajectories of spinning balls”

American Journal of Physics 57, 40 (1989); https://doi.org/10.1119/1.15864

Examines collisions between bat and ball as rigid bodies.

H. Brody. “Models of baseball bats”

American Journal of Physics 58, 756 (1990); https://doi.org/10.1119/1.16378

Examines collisions between bat and ball and the bat’s vibrations, treating it as a free object in space.

L. L. Van Zandt. “The dynamical theory of the baseball bat”

American Journal of Physics 60, 172 (1992); https://doi.org/10.1119/1.16939

Models the bat as a vibrating elastic mass with a normal mode.

R. Cross. “The sweet spot of a baseball bat”

American Journal of Physics 66, 772 (1998); https://doi.org/10.1119/1.19030

Compares the calculation of a bat’s “sweet spot” as the center of percussion or as a vibrational node.

A. Nathan. “Dynamics of the baseball–bat collision”

American Journal of Physics 68, 979 (2000); https://doi.org/10.1119/1.1286119

Presents a way to model the physics of the collision between a bat and a ball.

A. Nathan. “Characterizing the performance of baseball bats”

American Journal of Physics 71, 134 (2003); https://doi.org/10.1119/1.1522699

Introduces ways of measuring and modeling baseball bats in the physics lab.

R. Cross. “A double pendulum swing experiment: In search of a better bat”

American Journal of Physics 73, 330 (2005); https://doi.org/10.1119/1.1842729

Looks at the motion of a double pendulum and how it can model the swing of a bat or racquet.

R. Cross & A. Nathan. “Scattering of a baseball by a bat”

American Journal of Physics 74, 896 (2006); https://doi.org/10.1119/1.2209246

Examines the relationship between distance, speed, and spin of a ball hit by a bat.

R. Cross & A. Nathan. “Experimental study of the gear effect in ball collisions”

American Journal of Physics 75, 658 (2007); https://doi.org/10.1119/1.2713788

Looks at the possibility of whether slippage between surfaces in a baseball impact can be modeled like meshing gears.

R. Cross. “Mechanics of swinging a bat”

American Journal of Physics 77, 36 (2009); https://doi.org/10.1119/1.2983146

Models the force pairs at work in swinging a bat.

D. Russell. “Swing Weights of Baseball and Softball Bats”

The Physics Teacher 48, 471 (2010); https://doi.org/10.1119/1.3488193

Explores the moment of inertia of bats, commonly called the “swing weight” in sports writing.

A. Nathan, L. Smith, & D. Russel. “Corked bats, juiced balls, and humidors: The physics of cheating in baseball”

American Journal of Physics 79, 575 (2011); https://doi.org/10.1119/1.3554642

Examines the physics underlying several baseball controversies.

D. Kagan. “The vibrations in a rubber baseball bat”

The Physics Teacher 49, 588 (2011); https://doi.org/10.1119/1.3661118

Discusses some experiments with a rubber bat.

I. Aguilar & D. Kagan. “Breaking Bat”

The Physics Teacher 51, 80 (2013); https://doi.org/10.1119/1.4775523

Describes experiments with the breaking points of different wooden bats.

J. Kensrud, A. Nathan, & L. Smith. “Oblique collisions of baseballs and softballs with a bat”

American Journal of Physics 85, 503 (2017); https://doi.org/10.1119/1.4982793

Examines ball and bat collisions with a high speed camera.

K. Wagoner & D. Flanagan. “Baseball Physics: A New Mechanics Lab”

The Physics Teacher 56, 290 (2018); https://doi.org/10.1119/1.5033871

Describes a series of student lab activities to explore the mechanics of baseball.

And one final note, on balls rather than bats: new work in materials science is studying how softer materials inside solid projectiles can affect how they launch. Read all about it in this new post at the American Physical Society website:

Springy Material Boosts Projectile Performance https://physics.aps.org/articles/v13/160

 Update: And for those who read all the way to the end but are still upset about the lack of cute fuzzy bats: "What Bats Can Teach Humans About Coronavirus Immunity" at JSTOR Daily