Big Mo

During the nascent age of home computers, the Apple IIe football game Tuesday Morning Quarterback had a momentum indicator that fluctuated in favor of both teams throughout the game.  When momentum was on my side, short gains turned into long gains, touchdowns came easier, and life was good.  When on the opposition’s side, fumbles and interceptions became the norm and the odds of anything else going bad, along with my blood pressure rising, increased.  The concept of momentum in sports is well-known, lesser so, is the physics concept of momentum which has many application in sports and astronomy as well.

Momentum is defined as follows:

p = mv

Where p is momentum, m is mass, and v is velocity (both p and v are in bold as they are vectors with two quantities, magnitude and direction).  Thus, a marble rolling at 1 m/s has more momentum than a freight train at a stop.  And obviously, a freight train moving at 1 m/s has far more momentum than that marble at the same velocity.  A change in momentum over time also tells us how much force has been imparted on an object.  In more formal terms:

= dp/dt

In other words, force is equal to the rate of change in momentum divided by the rate of change in time.

Safer barrier after a NASCAR crash. Photo: Jared Smith/Wiki Commoms.

Safer barriers in auto racing use this concept.  Fatalities in racing used to be a fairly common occurence.  There were 37 fatalities during the first 57 runnings of the Indianapolis 500.  Improvements in auto design, head restraints, and the safer barriers have dropped those numbers considerably.  The safer barriers act as a cushion to soften the blow of a race car against the wall.  What the barriers do is prolong the time of impact.  Looking at the equation = dp/dt, doubling the time of impact reduces the force imparted on the race car by one half.  The amount of time of impact is small, we’re talking milliseconds here, but enough to dramatically increase driver safety.  Another sport is grappling with the same concept, but with an impact that occurs inside the body.

Chronic Traumatic Encephalopathy (CTE) is a degenerative brain disease found in football players.  CTE results in memory loss, aggression, and early dementia.  The disease is the result of repetitive concussive blows of the brain against the skull.  The brain has some protection against common bumps in the form of fluid inside your skull, but the fluid gives way when a violent blow, such as often occurs in football, is taken by the head.  In effect, the inside of your skull lacks a safer barrier in these instances.  This shortens the time of impact leading to an increase in force directed to the brain.  And here you can see how problematic this is for football.  You can’t insert a safer barrier inside the skull, the answers lie in changing the game in a manner that reduces these impacts.  Really, the only solution at this point is to eliminate contact in the game, something that would radically alter the nature of football which has become the most popular sport in America.

Momentum also plays a role in rotational movement, which is applicable to a much less violent sport than football.

Angular momentum (L) is defined as:

L =Iω

Where I = moment of inertia and ω = angular or rotational velocity.

I varies by the shape of the spinning object but is proportional to the radius.

As angular momentum is conserved, if the radius of an object is reduced, its rotational velocity increases.  Figure skaters use this principle to create rapid spinning movements in their routines.  As the skater begins to rotate, the arms are drawn towards the body to reduce radius and increase velocity.  You can try this at home on a swivel chair.  Have a friend spin you around with your arms outstretched, then pull your arms inward.  You will note the rate of your spin increasing.  Not as much as a figure skater does, but enough to notice.

Imparting a rotational force on an object is referred to as torque.  If an object is malleable, increasing its angular momentum by adding torque to it will cause it to flatten.  You’ll see this at your local pizzeria when the cook takes a blob of pizza dough and spins it in the air.  The blob becomes flattened into a pie shape that is then cooked in the pizza oven.  Beyond Earth, there are many applications of this principle.

Angular momentum flattens protoplanetary disk around the star HL Tauri Credit: ALMA (ESO/NAOJ/NRAO), Yen et al.

Our Solar System originated when torque was applied to an interstellar gas cloud.  This force most likely came from a nearby supernova.  As the gas cloud began to rotate, it flattened and commenced the process of constructing the Sun in the center and the planets in the disk.  This process has been observed in other planetary systems in the formation stage.  How spiral galaxies originate is not completely understood, but a galaxy’s angular momentum causes it to flatten into the classic spiral shape we see in so many space images.  When galaxies collide, the reverse of this process takes place.

The Antennae Galaxies/NGC 4038-4039
The The Antennae Galaxies/NGC 4038-4039 colliding. Credit: NASA, ESA, and the Hubble Heritage Team (STScI/AURA)-ESA/Hubble Collaboration

When two spiral galaxies collide, the odds of their angular momentum being in the same direction during the collision is slight.  Think of it this way, kids often start a whirlpool in a swimming pool by walking around the perimeter of the pool in the same direction.  This torquing action increases the angular momentum of the water in the pool.  If some other kids jumped in the pool and starting walking in the opposite direction, this torquing action offsets the original whirlpool, causing the rotation of the water to decrease.  This is essentially the same thing that happens to spiral galaxies when they collide.  The result is the two galaxies merge to form a giant elliptical galaxy with little rotation.  In essence, this is pizza effect put in reverse as the two flatten spirals form a blob shape.

And how does this apply to us?  Well, not us directly, but in a few billion years, the Milky Way will collide with its nearest large neighbor, the Andromeda galaxy.  While the two galaxies contain over a trillion stars combined, the odds of the Sun colliding with another star is slim.  That is a consequence of the large distances between the stars.  If the Sun was the size of a basketball, the nearest star would be 4,300 miles away.  However, the collision will eject stars from their respective galaxies and gravitational disturbances could cause incoming comets to collide with planets.  As this event will occur billions of years from now, the Sun will be nearing its red giant phase meaning Earth has become uninhabitable.  Humanity will not contend with this event unless interstellar travel has been achieved.  The video below is a computer simulation of the collision.

So momentum is not just a phrase tossed around in “horse race” punditry, but an actual physics concept with applications in our daily lives and the rest of the universe.

*Image on top of post is Mike Stratton’s tackle of Keith Lincoln in 1964 AFL Championship game.  The tackle was a momentum changer both in the physical and allegorical sense as the play turned the game in Buffalo’s favor.  Credit:  Wiki Commons.

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