#centripetal force

Bucolic finger-picking melts into space rock overdrive on this latest album from Carrboro, NC ambient duo Tacoma Park. Imagine a Kluster song with a creek running through it, birds chirping, leaves rustling, the seam between glossy synthetics and down home organic sounds so faint as to be invisible.

Designer: Corleone

"The moon sets, and stars give way to daylight. But you are always there, at the center of the universe."

[Image description: a second tumblr ask from archaeopter-ace reading, “(though I definitely agree that the nuance of 'centrifugal force is a fictitous force' is absolutely lost in most physics classes, who are either 100% for or against its existence, and treating it like it's real means kids won't understand how force works properly. Force has to come from somewhere, it doesn't just spring forth from the ether because you need an opposing force to explain what you're seeing)”]

Okay, so bear in mind that I’m an upper division undergrad, and it’s entirely possible that I am missing some aspect that is taught in graduate level courses. Also, whenever I use the word “you” in here, I am using the general you.

So, first off, I’d like to clarify the reason why the imaginary number i* is used in many physics cases is the simple fact that it’s easier to take the  integral/derivative of e^(iθt) than it is to take the integral or derivative of sin(θt) or cos(θt). However, no matter if you choose complex exponentials or regular trigonometry, you will get a real answer. This is used for things that are periodic and repeating. Examples of this being used are masses on springs and pendulums, circuitry, and likely many more cases because so many physical systems can be measured as simple harmonic motion.

* Not to be confused with the unit vector î. This is associated with the very real x-direction.

However, in quantum mechanics, the imaginary number i is used for multiple reasons. It’s sometimes used as an exponent of the natural number e in order to avoid using trigonometry for the wave, but it is also multiplied across the entire equation Ψ(t) so that the solution is a real number.

Treating the centrifugal force as a force never makes the math easier, in my experience. However, depending on the frame of reference (aka point of view) you choose, you may or may not need to treat the centrifugal force as a force in order to make the math work.

For example, have you ever been spinning around a mass on a string above your head and then suddenly you let go while still trying to maintain that rotating circle? The mass you’re spinning flies off in a straight line in the exact opposite direction. This is due to inertia (aka the thing that keeps objects in motion staying in that same motion and objects at rest staying at rest unless an outside force acts upon them), although some may call this the centrifugal force. As long as you are in an inertial frame of reference (aka you aren’t accelerating), then the centrifugal force is not a force, but rather the effects of inertia. Newton’s laws of motion work perfectly to describe the motion of you and the object. It is much easier to deal with an inertial frame of reference than a non-inertial one. However, there are situations where the observer is in a non-inertial frame of reference.

Have you ever been driving and you made a hard right turn, only to feel your body shift towards the left of the car? That is not something that Newton’s three laws of motion can explain, not from your accelerating non-inertial frame of reference. They can’t mathematically model how you’re moving... not unless you invent a force that is pulling you towards the left side of the car! In that case, the centrifugal force is something to be treated as very real, and is equal to the mass of the object (aka you) times the squared angular velocity times the distance from the axis of rotation. Of course, someone sitting on the sidewalk (and not accelerating with respect to the Earth) watching you can conclude that you’re experiencing the effects of inertia and that there is no centrifugal force acting upon you.

Now, technically, one can make the claim that gravity is just as real as fictitious forces found in non-inertial reference frames. After all, if you’re in a windowless room and you feel like you’re feeling gravity like you would on Earth, how can you be sure you’re actually on Earth and not just accelerating through deep space at 9.807 m/s²? Einstein made that exact claim and it’s now known as the equivalence principle. However, I would ignore this unless one has to deal with general relativity.

(Other case of a fictitious, non-centrifugal forces in cars include how when the driver suddenly slams the gas pedal, you feel yourself thrown back against the chair. From an inertial frame this is the back of the chair accelerating forward into you, but from your non-inertial frame of reference there seems to be a force shoving you backwards. Likewise, when the car suddenly stops (whether intentionally or unintentionally), you’re thrown forward. From an inertial frame of reference, this is your inertia causing you to move forward even as the car stops. From your non-inertial frame of reference, it seems that there’s a force throwing you forwards. This is why you need to wear a seat belt, because even if you don’t get in trouble with the law for not wearing one, the laws of physics will get you if you’re in a bad enough crash.)

The Centripetal face...

Centripetal force is a contact force and contact forces fall under the electromagnetic force.

Centripetal force is the name given to any force which keeps a body in rotation. It is applied normal to the direction of motion and toward the center of rotation. This force can be either pulling (think a pendulum, the rope supplies the centripetal force) or pushing (think of the amusement park ride that spins and the floor drops). In both cases, something is touching the object in question to provide the force. This is why it falls under the category of contact forces. 

Contact forces also include things like pushing, pulling, and friction, although friction is very complex and cannot be attributed entirely to contact.

Now why aren’t contact forces their own fundamental force? Because nothing ever really touches. When two things ‘touch’, they are actually in electromagnetic equilibrium. The electrons in the atoms of the two objects are repelling each other with the same amount of force as whatever force is pushing the two together. Because of this, all contact forces are actually a result of electrons repelling each other, which falls under the electromagnetic fundamental force.

For more information: Wikipedia, Encyclopedia Britannica, and a helpful StackExchange post.

– Admin Noah