How to Twirl a Pen: The Physics of Looking Cool

A skill I’ve always found equal parts distracting and fascinating is the ability to twirl a pen between your fingers. After countless time of attempting this trick and looking like a fool, I realize this trick is all about the physics. As a newly enlightened physics student with a better understanding of rotational motion and friction, I tried breaking down this skill into its individual concepts in an attempt to teach myself.

Axis of rotation and center of mass: The key to setting up this skill is to balance the pen at its center of mass. The location of our finger at the pens center of mass acts as its axis of rotation allowing it to be fluidly swirled. Holding the pen at either end before spinning would take even more force to set into motion because there is more weight that needs to stay balanced parallel to the ground.

Friction: The next concept I realized is helpful is the fact that frictional force of our finger keeps the pen from falling to our palm and in keep the pen in motion by supporting the rotation. As a beginner pen-twirler I went in slow motion to practice the motion, and I found that wearing a glove increased the friction, which was helpful in the beginning twirls.

Rotational acceleration: After starting from rest, the thumb and forefinger making a snapping motion and it is the force of the thumb on the pen that applies the external force necessary to increase the rotational velocity and acceleration. This sets the pen into motion after which it should theoretically be caught after one rotation, or twirled between multiple fingers creating a cool illusion.

After an embarrassing number of attempts, while I realize I still can’t twirl my pen, I at least now understand the physics behind this mesmerizing trick (which is equally as cool).

The Power of Breakfast

Having won the world championships in sprint cycling, and standing atop legs 74 cm in diameter, Robert Forstemann is undoubtedly a powerful man. But how powerful, exactly? A recent youtube video aimed to answer this question in terms of Robert's favorite breakfast item: toast. By attaching a 700w toaster to his stationary bike (along with a bunch of physiological measurement tools) we are able to see the exertion needed for that slice of golden-brown deliciousness (I, too, am a huge fan of toast).

Let's lay out our knowns and state assumptions. Robert maintains his level of exertion for 58sec, after which the bread pops up. The toaster is rated for 700w, meaning that for the duration of this time Robert is providing at least 700 watts through the bike. Let's assume he is doing the bare minimum. If you watch the video, here: https://www.youtube.com/watch?v=S4O5voOCqAQ obviously it is tiring, but numerically let's see.

So, Robert didn't really even earn his toast, as long as we are assuming standard white bread without butter (though everything is better with butter). Talking about cycling so much in class lately reminded me of this video, but the brief analysis above puts in perspective the luxury of power provided by an outlet. Imagine if we had to hop on a bike or do a bunch of burpees to power all of our cooking. Yikes. 

The Physics of an Achilles Tendon Rupture

Recently, I had the unfortunate experience of rupturing my Achilles tendon during an intramural soccer game. Having played competitive soccer for most of my life without experiencing any sort of significant injury, I find it very ironic that such an injury finally occurred during a noncompetitive intramural game.

My injury happened on cold fall day right after half time of the second game I was played that day. Stupidly, I did not stretch after half time and believe that while resting during half time my muscles really tightened up due to the cold weather. A few minutes in to the half, the ball was played to me and I turned with it while sprinting and changing direction. At this moment, I experienced what felt like someone kicking me as hard as they possibly could in the back of my calf. I subsequently went to ground and rather painfully noticed that my calf was cramped up and stuck all the way up below my knee. I was eventually able to pull the cramp out and hobble off the field. At first, I was convinced that someone on the other team had kicked me in the back of my leg and that had caused my cramp. However, having talked to my friends on the sidelines they said nobody was behind me so the feeling of getting kicked was due to something else. As a result of this, I thought maybe I had torn my calf or had some sort of deep tissue bruise.  Although initially I did not think my injury was too significant, I decided to go see the doctor. At the doctor's office, it took maybe 2 minutes to diagnose me with a ruptured Achilles tendon.

Ignore air Resistance

As a student of physics, I have recently spent some of my free time wondering what kind of force the ground must have exerted on my Achilles in order to tear what apparently is the strongest tendon in your body. According to my doctor, an Achilles is able to receive a load stress that is 10 times your body weight. It receives a load of 3 times your body weight while walking and 7 times your body weight while running. With this being the case, let’s try to analyze the minimum tension force that I placed on my Achilles when it tore:

Mass: 85kg

F_total= 10(85kg)(9.8m/s²)= 8330 N

F_x=10(85kg)(9.8m/s²)Cos(70)= 2849N

F_y=10(85kg)(9.8m/s²)Sin(70)= 7827N

Additionally, when your Achilles tendon snaps in makes a very loud sound that is similar to a gunshot. Some of my friends thought they heard a loud snapping sound when I went down on the field, but at the time did not realize where the sound was coming from. With this being the case, let’s try to estimate the velocity with which my tendon snapped:

W_net= ΔKE

F_total= 10(85kg)(9.8m/s²)= 8330 N

Distance (estimate)= .25m

Mass tendon (estimate)= .2kg

Fd= ½ mv²

(8330N)(.25m)= ½ (.2kg)v²

v=144 m/s No wonder it is so loud!

The Physics of Curling

As a captain of the curling team, I am always looking for ways to improve our game; thankfully, I think what we’ve learned in Physics 111 this year will help us defend our national ranking.

The other think to consider is when we’re trying to throw take out shots. Below is a video of some really impressive take out shots:

https://www.youtube.com/watch?v=iYcYaUBaEeI

In my opinion, the take out shots are the most fun to throw, but getting enough velocity on the stone can be difficult.  In relating initial and final velocities of each stone, we can assume that the stones experience a perfectly elastic head-on collision (they make a noise when they collide, so energy is not technically conserved), ignoring the static friction between the stone and the ice.

When curling, the stone that is hit (1) has an initial velocity of 0 m/s, and the stone doing the hitting (2) has a final velocity of 0 m/s. With this, we can see:

which means that the stone that is hit leaves the collision with the same velocity as it was hit with (in reality, slightly less) in the same direction of motion as the hitting stone. Because the stones are moving around 2 m/s at this point, the house (scoring region on the ice) has 3.5m radius, and velocity is proportional to distance traveled, this time not ignoring friction, a change in 1 m/s in either direction can mean the difference between hitting the stone out of the house, or having it stick around. This difference in distance traveled can mean the difference between scoring in the end, or losing the end, which will have major ramifications in point totals for the game, and throwing order for the following end.

                Another aspect of curling that physics can explain is the importance of sweeping stones. When a stone is thrown, if it does not have the correct initial velocity for the type of shot you are trying to make, sweeping the stone can make the stone travel farther. How can this be so? Conservation of energy:

If we are trying to see what makes the stone go further without having changed the initial velocity, then the only variable that can logically be changing is μ. Sweeping melts the pebbles on the ice, thus lowering the coefficient of friction, which is what makes the stone go farther when it is swept. Another interesting and less understood part of sweeping, is that it makes the stone curl less; this might be better understood if we look at why a stone curls at all.

Although there is a lot of curling that Physics 111 can explain to us, there is one thing that is still not understood about curling: why it is that the stone curls in the direction of motion? If you were to push a spinning cup on a flat table, the cup would ultimately curl in the opposite direction of the cup’s spin. So  why doesn’t the curling stone do the same thing? The answer is in the pebbling of the ice. This video does a good job of exploring why it might be so:

https://www.youtube.com/watch?v=7CUojMQgDpM

The short answer: we don’t really know why it is, but hopefully, as we move into rotational motion, we’ll be able to understand better the physics of curling.

Jonah Lomu: A Force to Be Reckoned With

At 270 pounds during his playing career, Jonah Lomu was the average size of a rugby prop. Props tend to be some of the strongest players on the field, but they are certainly not known for their speed. A rugby wing is normally one of the smallest players, yet fastest, players in the game. Lomu defied the norm by being both one of the largest and quickest players on the field. He was known for this incomparable combination. In high school he ran 100 meters in 10.8 seconds. For comparison, Usain Bolt ran it in 9.63 seconds. The slowest man in the 2012 olympic final ran it in 9.98 seconds. Lomu's speed is extreme when the sheer size of this body is taken into account. Rugby wings are also not normally world class sprinters; they must have a combination of agility, speed, and technical skill. Lomu had all of this as well as brute strength.

The following video shows Lomu's strength and speed in a collaboration of his greatest tries (a "goal" in rugby). It also has cheesy, inspirational music. Lomu is the man wearing a jersey with "11" that repeatedly plows through other players. 

https://www.youtube.com/watch?v=OsXTa7UCGlk

(Photo from: http://www.telegraph.co.uk/sport/rugbyunion/international/newzealand/11210454/Jonah-Lomu-is-the-Muhammad-Ali-of-rugby.-Julian-Savea-will-never-match-him.html)

Jonah Lomu is considered one of the greatest wings of all time. He was such a force to be reckoned with because of a combination of his speed and size (pun intended). His mass was about 100 pounds greater than the average wing, 150-180 pounds versus his 270. Because Force=Mass*Acceleration, and Jonah Lomu had both the ability to accelerate very quickly and a high mass, he acted with a much greater force than the average wing. 

In Rugby, defense is set up in a way that normally a position will normally defend against own position on the other team. The tackler should have a greater acceleration than the ball carrier because the tackler will have had a quick burst of speed to meet the ball carrier who has already been moving at pace. An average wing will be in somewhat similar mass to his opposition. The tackler will exert a greater force on the ball carrier because of the increased acceleration and similar mass.  This will enable them to complete the tackle or slow the ball carrier enough for additional defenders to do so. Jonah Lomu had such a great mass, that even if the tackler had a higher acceleration, Lomu would still exert a greater force. He would simply storm through defenders, using an incredible stiff arm to easily push them aside. 

(Photo from: http://physicsinrugby2012.weebly.com/kinetics-and-forces.html)

Not only did Jonah Lomu exert a greater force on the other wings, he also moved with a greater momentum. He had both a greater mass and a greater velocity than the defender he would encounter. Defenders have a high acceleration because they are normally acceleration from rest to meet the ball carrier from the off-side line. The defender will have a lesser momentum, though, because they will not have reached a speed as great as the ball carrier who would have been moving at pace from a deeper position. 

(Photo from: http://ncvs.org/e-learning/equations/chapter2/index.html)

The picture below shows how defense is set up. The wings (number 11 and 14) will be set in a staggered line, and the ball will travel down the line while the players run forward. The wing will catch the ball while already sprinting, and try to run up the side through the defense's flat line. The defense will be stand on the off-side line (imaginary flat line across the field) and accelerate from rest to meet the attacking players. 

(Photo from: http://www.wilkesbarrerugby.com/theGame/)

The 1995 world cup final was played between South Africa and New Zealand. South Africa practiced specific defending when dealing the Jonah Lomu. They would herd him to the side line with multiple players attempting to make a tackle at once. This left the far side of the field more open with an outnumbered defense. However, it was the only way to stop Lomu from scoring try after try. 

http://www.olympic.org/olympic-results/london-2012/athletics/100m-m

http://physicsinrugby2012.weebly.com/kinetics-and-forces.html

http://blackbeltwhitehat.com/2015/10/02/rugby-world-cup-2015-size-height-weight-speed/

The Physics of Popcorn

The Physics of Popcorn

What are the forces that make a round corn kernel into a fluffy piece of popcorn? It is a perfect example of how physics can apply to all things—even a snack for your favorite movie. I also have special interest in this due to my experience in concessions where popcorn is a big seller.

So far, food engineers have determined that popcorn kernels pop most efficiently and consistently when water is 13.5-14% of the kernel’s weight and when the kernel is close to the shape of a sphere (due to a more even distribution of force). Using these statistics, food engineers have been able to reduce the rate of unpopped popcorn by 75% since 1950. A kernel of popcorn is made up of a hull that surrounds the seed, a protein matrix called the endosperm, and the germ.

When heated, the water inside the kernel turns into vapor, which forces its way into the endosperm to make a hot doughy mixture. The continuation of heat causes the pressure to build up, which causes the hull to burst, and the endosperm/steam mixture to burst. This mixture cools once outside of the kernel. The pop is not caused by the breaking of the hull, but by the release of the steam.

Gas laws that state that volume is proportional to temperature divided by pressure can explain this process.

As the temperature increases, the volume increases, and thus the pressure increases. The gas pressure builds up to give a force that will break the hull. Gas pressure is defined by NASA to be a scalar quantity that is the measure of the linear momentum of the gas molecules. In other words, the gas molecules that are bouncing off of the walls of the hull are imparting a momentum on the surface. This means that gases produce a force that is perpendicular to the surface (a normal force). This force allows the water vapor to mix itself with the endosperm that produces the popcorn.

When the popcorn pops, it is launched into the air by the emergence of the endosperm “leg”. The angle of this launching causes the popcorn to move in a circular motion in the air, being brought down by the force of gravity. The leg provides an initial velocity, and the popcorn has acceleration throughout the entire rotation because it is changing direction.

http://chemistry.bd.psu.edu/jircitano/gases.html
https://www.grc.nasa.gov/www/k-12/rocket/pressure.html
http://www.latimes.com/science/sciencenow/la-sci-sn-popcorn-science-20150210-story.html

Figure skating safety

As a member of Colgate Figure Skating Club, I was asked to complete a baseline concussion test a few days ago because Figure Skating was classified as a higher risk sport by Colgate Student Health Services. This test and the concern on figure skating safety remind me a severe collision incident happen last year at Grand Prix Cup of China.

During the six-minute warm-up session prior to the men free skate, where all the skaters in the group (usually five to six) prepare on the ice at the same time, Yuzuru Hanyu and Han Yan crashed into each other at a very high speed. The Collision happened while Yuzuru was preparing for a jump, skating with his back to the ice and both of them had little time to attempt a brake. They both laid on the ice after the collision. Han was able to stand up and get off the ice by himself, but Yuzuru, who experienced more severe head trauma, laid on the ice for a minute with blood streaming down his chin and neck before the medical corps reached him.

https://www.youtube.com/watch?v=Jf84VzlzLhI

How can this mild and elegant sport result in such severe injury that is not even common in the more intensive sport like ice hockey?

We can think about this question in two different ways: Energy and Momentum.

From the energy perspective, both of the skaters had large kinetic energy because they were skating at an enormous speed.

They experienced a sudden stop during the collision and their kinetic energy got into zero. Even though part of the energy lost due to the non-conservative force interaction (for instance friction force, air resistance), the majority was still absorbed by the two skaters, resulting in the trauma injuries or even the contusion of the organs. However, in ice hockey, all the players are required to where helmet and personal precaution gear. The equipment can transfer the kinetic energy of the player into the potential energy as it experiences shape change and thus minimize the energy transferred to the player himself.

From the momentum perspective, both of the skaters as they skated in very high speed had large momentum:

After we introduce the concept of impulse which equals to the change of momentum we know that:

Since both of the skaters were wearing figure skating customs that cannot serve as cushions, the time for the collision was very short, resulting a very large force that acting on the skater. In ice hockey as everyone is wearing protective equipment, the cushion can decelerate the players in a more mild way and lengthen the time, resulting a much smaller force acting on the players.

To everybody’s shock, 40 minutes after the terrible crash, both Han and Yuzuru showed up and performed their free skate. Yuzuru, who experience the more severe injury and even confusion, fell for five times and ended up getting the second place. This action definitely manifests the spirit and strength of athletes even though personally I feel that they were risking themselves to the chance of exaggerating their injuries.

https://www.youtube.com/watch?v=EFwEHecrC60