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Chapter Text

Some Kinematic Equations for Reference:

Ok so time is the chill, popular kid. There’s no life in the party without them there. (there might be no life at all) Like, they’re in every kinematics equation, tff??

Final Velocity is the twin that kind of lacks a personality. They’re like that one emotionally hurt variable that doesn’t have a personality anymore because of the harsh world.
Initial Velocity is the twin that is shy, sometimes getting excluded from the equation. But both sides seem to be very important. They seem to be rich and people like them because of that. They actually are happy to be included.

Acceleration used to love time, but then they lost the love and started loving velocity (both of them. Yeah. They're traumatized.)

Position is the needy popular variable, but they really are needed this time. Always looks so stressed because they are plagued by their paralysis demon. They’re personality changes so much depending on the day, bu it’s welcomed by their friend group.
Displacement (Position’s sleep paralysis demon; the difference between them is sometimes a lot but most times it’s not that much)

Okay, so final velocity was first adopted by time and acceleration, but then they split up (a/t) (but they’re still in the friend group; just bad terms) and then final velocity met position. They clicked immediately when final velocity learned their personality and started liking a traumatized variable.
(initial velocity usually gets shunned out in these situations, they're quite the silent one) 

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So the traumatic kinematics gang is all here. They used to have their differences, but then they made up, y'know? So when are they the stars of the show? 

Primarily, of course, it starts with the harem-lover Acceleration. Yes, they can't choose between which one of the two rich Velocity twins to be with. For the kinematics group to function, however, acceleration needs to be mentally stable--they're pretty important, not gonna lie. 

And since the group is quite literally the most unstable thing in the world (one member has a paralysis demon, the other few are traumatized in love triangles [hexagons]), they need to be used when something is going in a straight line. Anything else--welp--I don't think they'd be particularly useful in that context. 

Of course, they can tackle things on their own. But that's rare, and they prefer to stick together after all that has happened to them.

When it comes to free-fall, there needs to be a change. Gravity always acts downward, no? 

So in the light of a projectile, acceleration goes and becomes the hero. It knows exactly what to do now. Setting their love triangle aside, they take the great value of downward.

This is because, according to Newton's second law , Gravity (acceleration but better) is a Force and a force acting on an object causes it to accelerate. 

AAAANNNDD who cares about air resistance?~

Anyways, onto the units. Since acceleration is the rate of change of velocity (distance traveled divided by time), it's the rate of change of the rate of change of distance traveled! Therefore are the units for the acceleration due to gravity (often called g).

Think of g as a's alter ego. g is the acceleration due to gravity, and a is just...acceleration. Pure in its natural, traumatized form.

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So we learned that small g is the acceleration of an object attracted b earth to its center with a force of, where we replace a with g because I'm too lazy to get the html script again! m is still the mass of the object. 

The F is the gravitational force. 

But...gravity is not all just on earth. Acceleration (pretend they're existent and not a thought) is attracted to both velocities (ditto). In space too. What? How do we measure that?

Enter, the law of Universal Gravitation.. This big bad boy seems scary, but it's just what we need to measure the force of attraction between two bodies, neither of those that are the Earth. 

Professionally, it says: every point everywhere is attracted to every other point by the multiplying of their two masses first and then dividing it by the distance between them.  Squared. 

Big bad Fg is still the gravitational force, M1 and M2 are the massive big bazonker masses, and r is the distance. Make sure it's squared!!

From this, we can see that: Mass big, Gravity big. Radius big, Gravity not Big. 

Oh yeah, the big bazonker G? It's uhh

uhhh...

It's hard to explain. It's one of the laws of nature. God just went bing bap bong bom bop bop bam, and poof, out came . Ehh, the units are too scary, I think we can just probably turn a blind eye to them until they actually matter. It just allows the formula to be used universally. I mean university. I mean universally. ο(=•ω＜=)ρ⌒☆

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Alright, so my beginning chapter of the Law of University Graduation isn't enough. Let me explain better. . Here is the Law of University Graduation. I mean Universal Gravitation. Graduation. Forget it, we need to experience both anyways. 

So! The force between two objects of mass M and m separated by a distance of r is represented by the Law of Universal Gravitation. 

G is the gravitational constant, which is 6.67 E -11, in some weird units. For this AP exam, let's hope to never ever use them. How do you get this big thing, you may ask? Literally no clue. Cheers. 

The force acts on both objects. 

From the Law of University Graduation we can determine that, hey, wtf?

For every time we solve for the gravitation on earth, we don't need that big ass equation. We are actually all relatively the same distance from the core of the earth as someone on the other side of the world! So technically the r can be constant!! OMG!!

Wait, isn't the Mass of the earth constant, too?? HOLY SHIT!! 

So since the values of M and r are constant in terms of the earth, we can combine that with the other constant G to form, viola! 

, where g is 9.8 m/s^2 and m is whatever the hell you want it to be. 

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If you're anything like me bro, you went into your first year of high school with a singular AP class: AP Human Geography. In that class, you learned about sus-system-inc farming, China, and retirement homes...

and you also learned about centripetal and centrifugal forces!

One way my teacher taught me how to differentiate between the two: one was like "damn, nice pretty flower petal" and the other one was cetnri-fuck you, respectively. I think you can get which one's which.

Okay, so now we know that centripetal-s are nice and sunny and flowery and rainbow-y. But what the hell is it in physics? 

since forces in general are neat, net forces in general are also really neat. Net forces are the sum of all the forces. Like just add 'em all up. Net, amirite? (neat? No laughs?) (‾◡◝)

Okay, so the centripetal force is basically just the net force that acts towards the center of the circle that the object is making. There is no new FORCE, per se; centripetal (forces) are legitimately three cats in trench coats. The cats being literally any other force. Add 'em all up, see if it's goin' around, and whoa lookie there! My gosh...

...

That sounds hella confusing. Actually, think of it like this:

When you whirl something around on a string, like a yo-yo. What is making it go in a circle? the gravity always goes downward. So what gives?

The STRING, of course!

The string makes it go 'round. It's attached to where you're holding it. 

When you go on a roller coaster and empty your stomach on one of the loops. What is making it go in a circle? THAT'S DAMN RIGHT!!

the NORMAL FORCE! 

It prevents you from falling off and into the damn coaster, sure, but you know what it also does? IN A FREE BODY DIAGRAM, IT POINTS TO THE DAMN MIDDLE OF THE CIRCLE!

Aaand since to good 'ol , we know that, whoa, the force and the acceleration have to be parallel. Proof for the nerds: one is scalar, one is vector. 

soo... whoa! The force...it's pointin' to the middle... and acceleration... it also must point...where? To the middle, of course! Boom!

OK, so you mentioned something about my popular harem-lover variable acceleration. 

Why are they here? the speed is not changing...?

Oh yes it is! Remember that velocity is a vector! 

Therefore, the velocity changes, and since acceleration is velocity over time, it has to change too! It's nonzero! 

Yippee!!

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In Simple Harmonic Motion, there is one thing that you really need for all of the traumatic experiences in Physics: 

--Equilibrium. Pure, blissful peace.

But this is Physics we're talking about. The school air could kill a Victorian child or two--that's what we have to deal with every day. But luckily, in this Unit, we have one companion by our side! Enter, the Restorative Force. They're gonna be with us for the remainder of this Unit, so see them around!

They're like--a necessity. Like, you can't have simple Harmonic Motion without them in the bleak lands of knowledge. Heck, it'd just be simple motion, there is no harmony when they're not around! 

Okay, now we have established that a Restorative force is needed for equilibrium. But damn if every question was equilibrium, that'd be good...

Unfortunately, it's not. Sigh. The restorative force needs some help. 

In the two tested scenarios on the AP exam, Springs and Pendulums. They each have their own personalities. 

In springs, the restorative force is different. They're sassy, and they make decisions solely by reverse psychology! They're like a little kid-- Hmph!! Oh, your displacement is that way? fine. My spring constant is the opposite--Fuck you!! 

They're so stiff. Like they don't budge on their decisions. The spring constant (k) is actually a measure of their stiffness, in this respect. Higher hmphability, the more it takes to move them! Hmph...

The time it takes for a spring for one full oscillation and come back to where time first started being recorded is given by the following equation, where T is the period, hopefully in seconds; m is the mass, and k is the spring constant. 

The reciprocal of this (where we flip the table) gives us the frequency of the oscillations.

On the other hand, we have pendulums. The restoring force is scared of the pendulum, actually--they take another form to interact with them: the gravitational force. Coward! They hide behind the likes of the existent gravitational force??? 

Furthermore, the pendulums are so frightening that the restoring force only stays with the pendulum for angles less than 15 degrees. They're so...spontaneous. 

The time it takes for a pendulum for one full oscillation to come back to where it was since time first started being counted is given by the following equation, where T is the period, L is the length of the pendulum, and g is the acceleration due to gravity, which, when not in the Earthly confines of..well, Earth, is given by the Law of Universal Graduation. That's something that Google will bless you with (or my previous chapter (p≧w≦q))

The reciprocal is, once again, frequency. 

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Everything starts with the god of all creation, good old Sir Isaac Newton . It is in my belief that the name Isaac–in Hebrew–meant “to laugh”. Well, the only thing i’m laughing at is the fact that i’ll probably do bad on that test! Haha… hahaha.. Anyways.

So, Newton made some rules for life. It matters not how he got them, Physics 1 only tests on how they work. We’ll learn the rest later, in due time: 

• The Law of Inertia: Big funny word! It’s alright, just remember it as IF OBJECT NO ACCELERATION, OBJECT HAS NO FORCE ON IT and will keep moving that way unless some other force is upon it. It can be algebraically written as 

• • Some history because that's what helps: So the early Greek and so thinkers were like "ZAMN! The natural thing for all y'all baddies [objects] is to go to rest" because they didn't know that friction existed. And then my boy Galileo Galilei--GG--was like, "nuh-uh!" and then did some magic and transformed. Remember that the world is an imperfect place, and AP Physics 1 is. Ha ha ha ha! ha...

• The Law of Dynamics: It's quite literally the first equation, just remove the 0. 

• • It just says that the force is proportional to its acceleration. The DERIVATIVE of MOMENTUM (p) with RESPECT TO TIME (t) is just the definition of some other variable we'll see in the future. See, it's all interconnected! :3

• The Law of Action-Reaction: If an object has a crush on another object, the other object is going to reciprocate feelings towards them, equally but like, you know, to the other side (Bruh selfcest was one of the words that i have learned this year), so the equation might look a little like: (IDK LaTeX)

, bur only when. REMEMBER SELFCEST IS NOT GOOD IN PHYSICS GUYS, but i guess it doesn't really matter unless you're locked in...

Alright, now that we have the Laws. Remember, these laws ARE ALWAYS THERE. I was solving a question about fluids one day, and it was like "If you stick a brick in a dense liquid denser than the brick (hypothetically), would the thing containing the brick feel a force from the liquid?" I was like, no, because when I stick my hand in water in a bowl, the bowl doesn't break. BUT IT STILL FEELS A FORCE, NO MATTER HOW SMALL. I got it wrong. 

okay. Now for the next constants. But we first need to know how physics works. Yeah, i know. 

PHYSICS IS ALL ABOUT INTERACTIONS.

PHYSICS IS ALL ABOUT INTERACTIONS.

PHYSICS IS ALL ABOUT INTERACTIONS. 

ok, lastly,

PHYSICS IS ALL ABOUT INTERACTIONS. 

ok. 

Now (:3) here are the list of tested forces in AP Physics 1 as of 2025:

Gravity:, where  is the mass,  is the CONSTANT that is the acceleration due to gravity (usually 10, but 9.8 if you're doing an FRQ). 

• • You can see that the units of mass are kg, and the units of g are m/s^2, ergo:= Fg. Which are coincidentally the units for a Newton!)

Springs: , where 

is the spring constant (how stiff the spring is, higher=stiffer), and is the distance from the point where the spring is in equilibrium. The negative means that the vector force is directed TOWARDS WHERE THE SPRING IS IN EQULIBRIUM!

Normal: The force that is perpendicular (Definition of Normal) to the force acting on it. the Force can be WHATEVER, and the sole purpose of the normal force, once you're familiar with it, is to stop the object from fucking going through the floor. :3 

• It's denoted by capital N, as you can see in the friction units. 

Tension: There is no formula for this, it's simply an attractive force between the object and some other thing. It's quite literally anything, most likely a string or something. Just anything. Really. That moves the object. 

Friction: MOSTLY NEGLIGIBLE IN CASES OF THE AP PHYSICS 1 EXAM. 

Static Friction:, where the force is directed opposite of physical movement. It's the force that restricts the movement from the start, and it is present when the object is at rest. 

• In our imperfect world, the bottom of blocks have rivets and ups and downs, and the force of static friction is the force required to break these bonds to set the blocks moving on the ground. That's why it has a less than or equal to; the force (static friction) needs to be counted as LESS THAN OR EQUAL TO the coefficient of static friction and the normal force, lest it be MOVED (le gasp) and it turnes into the GHASTLY KINETIC FRICTION. 

Kinetic Friction: , now the bonds are broken! We now have a nicely moving block, but there are still rivets on the floors, i guess. bummer. 

Some Fluid Forces, Pressure: What is pressure? Pressure is Force exerted over an Area. It can be seen as , and usually is seen in the NEW AND MAGICAL fluids section of the AP exam. 

That's all for today folks, come next time.