Learn Physics through Songs - Lesson 7: Vectors

Vectors have both magnitude and direction,
Like forces and velocity, that's the connection.
Scalars have just magnitude, plain and clear,
Like time and speed, there's no arrow here.
To add vectors, head to tail them,
Or in components, it won't fail 'em
To subtract, just flip and add,
It's called the resultant, and that’s not bad.

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Vectors The Musical

Learn Physics through Songs - Lesson 6: Gradients

The Gradient is the slope of the line,
Divide change in y by x, you'll be fine.
Trend lines pass through the error bars, 
curved or straight, the knowledge is ours.
Max and min gradients, through error bars they go,
For curved graphs, use a tangent line, yo.
Rise over run, the gradient is done!

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Gradients The Musical

Hey, want to learn about motion with me?
The basics of how stuff moves, let's see.
We'll cover the key terms and motion graphs too,
So by the end, this'll all make sense to you.
Position's a location from origin's place,
Displacement, the change in position's space.
Distance is scalar, just how far you've gone,
Velocity combines speed and direction as one.
Acceleration's the rate velocity changes,
Change in velocity over time it gauges.
Oh, you like motion graphs? Cool!
Slopes and areas, are the rule.
Ready for the journey? Here we go,
With these tools, you'll soon know.
The slope of position, is velocity,
Do it again and its, acceleration you see,
Under A, V's change is found,
Below velocity, displacement's bound.

Motion Graphs The Musical

S-U-V-A-T
Kinematic equations, can't be beat

S is displacement, U initial speed
V is the final velocity you might need
A is for accelerating, changing the rate
And T is the time, its duration mate
 
S-U-V-A-T
Kinematic equations, can't be beat

First, read that question, imagine the setting Then note what they're giving, no data fretting
Whichever kinematic formula suits the deed
Plug and chug, victory is what you'll breed!

S-U-V-A-T
Kinematic equations, can't be beat

S-U-V-A-T

In the world of measurements, we must be wise,
Two types of errors, we can't disguise.
Systematic error, a constant foe,
Shifting our data, makes the y-intercept grow.

Systematic error, a calibration's curse,
Forget to Zero the scale, will make it worse.
Random error, we can tame,
With more trials, our results won't be lame.

Systematic & Random Error Song

When one goes up, the other too, a constant ratio they pursue.
The origin is their starting place, a straight line it will trace,
Check the ratios, if they're the same, 
then directly proportional is the name.

Directly Proportional

One bullet fired, one bullet dropped. 
Same time landing, physics can't be stopped.
Why does that happen? Let's break it down,
Projectile motion, it’s the talk of the town.

The x and y components, treat 'em separately,
If air resistance is negligible, here's what to see,
No acceleration in x, just keep it steady,
In the y, it's -9.8, so get ready!

Graph it like a parabola, symmetrical and sweet,
Velocity up matches velocity at the feet.
At the top, y velocity hits zero, see,
Acceleration's still there, and always will be!

The x and y components, treat 'em separately,
If air resistance is negligible, here's what to see,
No acceleration in x, just keep it steady,
In the y, it's -9.8, so get ready!

Projectile Motion

Verse 1)
Drop it down, watch it fall,
Acceleration starts at 9.8, that's the call.
Gravity's pullin', feels so strong,
But there's more to the story as it goes along.

(Pre-Chorus)
Speeding up, air resistance fights,
Pushin' back with all its might.
Faster it falls, the stronger the force,
Balancing out in due course.

(Chorus)
Reaching terminal velocity,
Where the forces find equality.
Air resistance, weight, they’re in sync,
Acceleration drops to zero in a blink.

(Verse 2)
As it falls, the speed will grow,
Air resistance starts to show.
Climbing higher, pushing back,
Gravity and air, on the same track.

(Pre-Chorus)
Speeding up, air resistance fights,
Pushin' back with all its might.
Faster it falls, the stronger the force,
Balancing out in due course.

(Chorus)
Reaching terminal velocity,
Where the forces find equality.
Air resistance, weight, they’re in sync,
Acceleration drops to zero in a blink.

Terminal Velocity

(Verse 1)
Newton’s first law, here we go,
An object at rest, it's gonna stay so.
In motion, it keeps a steady pace,
Unless a force comes to change its place.

(Pre-Chorus)
In translational equilibrium, it's the deal,
Forces balanced, nothing to feel.
No acceleration, steady as can be,
Inertia keeps it right, just wait and see.

(Chorus)
Newton's laws, they’re here to guide,
Three simple rules, physics by our side.
From rest to motion, forces all around,
Newton's laws, they truly astound.

(Verse 2)
Newton's second law, it's F equals M A,
Force and mass, acceleration on display.
Push harder, see the speed increase,
More mass the change won't be a breeze.

(Chorus)
Newton's laws, they’re here to guide,
Three simple rules, physics by our side.
From rest to motion, forces all around,
Newton's laws, they truly astound.

(Verse 3)
Now the third law, action, reaction pair,
Every force you give, there's one right there.
Equal and opposite, that's the key,
Push or pull, it comes back equally.

(Bridge)
Picture a truck hitting a car, forces collide,
Equal and opposite, on either side.
The truck feels the force, the car does too,
Newton's third law, it's always true.

(Chorus)
Newton's laws, they’re here to guide,
Three simple rules, physics by our side.
From rest to motion, forces all around,
Newton's laws, they truly astound.

Newton's Laws

(Verse 1)
Let's talk friction, it's all around,
When two surfaces meet, it’s where it's found.
Sliding and static, two types to know,
One keeps you steady, the other lets you go.

(Pre-Chorus)
Static friction holds you tight,
Keeps you in place with all its might.
It's always stronger, that's a fact,
Until you move, it’s got your back.

(Chorus)
Friction's here, it’s in our sight,
Two surfaces in contact, holding tight.
Static strong, sliding weak,
Coefficient’s the key we seek.

(bridge)
The friction force, it’s μ times normal,
μ's the coefficient, in the formula.
Normal force, is always perpendicular.
Friction's equation, is always spectacular

(Chorus)
Friction's here, it’s in our sight,
Two surfaces in contact, holding tight.
Static strong, sliding weak,
Coefficient’s the key we seek.

Friction

(Intro)
Inclined planes, they're all around,
Physics playground where solutions abound,
From slopes to hills, they shape our view,
Let’s delve right in, there’s much to pursue.

(Verse 1)
Gravitational force, we break it up,
Parallel and perpendicular to the plane,
Free-body diagram, let’s draw it out,
Separate the forces, without a doubt.

(Chorus)
Find the Parallel weight with M G sine theta
Perpendicular weight is M G cosine theta
On an inclined plane, 
we slide, slide, slide. 
we slide, slide, slide. 

(Verse 2)
Newton’s law, net force, we’ll find,
In our coordinate system, perfectly aligned,
Trigonometry helps, angles in play,
Split the components up in that way.

(Chorus)
Find the Parallel weight with M G sine theta
Perpendicular weight is M G cosine theta
On an inclined plane, 
we slide, slide, slide. 
we slide, slide, slide. 

Inclined Planes

(Intro)
Listen up, my friends, let me tell you a tale,
Of momentum and impulse, a story to unveil.
Momentum is mass times velocity, you see,
A measure of motion, as simple as can be.

(Chorus)
Collisions! Collisions! 
Trains to crumple zones! 
Impulse is the change in momentum
change in momentum. 
Impulse is the change in momentum. 

(Verse 2)
But what about impulse, you might ask?
It's the change in momentum, a fundamental task.
When you jump in an airbag, it extends the time,
Decreasing the force, a safety paradigm.

(Chorus)
Collisions! Collisions! 
Trains to crumple zones! 
Impulse is the change in momentum
change in momentum. 
Impulse is the change in momentum. 

(Verse 3)
The rate of change of momentum, a concept so true, 
Is equal to the net force, a fact for me and you. 
Finding the impulse, a task of great skill, 
The area under a force-time graph, a thrill.

(Chorus)
Collisions! Collisions! 
Trains to crumple zones! 
Impulse is the change in momentum
change in momentum. 
Impulse is the change in momentum. 

(Outro)
But momentum's a vector, so listen here,
When handling rebounds, this fact is clear. 
Find the sum of the speed before and after
This is the change in velocity you're after. 

Momentum and Impulse

Intro:
Verse 1:
Alright everybody, listen up close,
Momentum conservation, here;s how it goes.
Momentum of a system, constant will be,
Unless an external force acts, you'll see.

Pre-Chorus
In collisions and explosions, this law holds true,
Momentum must be conserved, through and through.
And in two dimensions, a separate fact,
X and Y momentum, must both be intact.

Chorus
Elastic collisions, more of the same, same.
Momentum energy, remain the same same.
But inelastic impacts, are more lame, lame. 
Only momentum remains the same, same.

Verse 2
Solving these problems, easy as can be,
Set the momentum before, to what it will be.
But Momentum's a vector, you can't forget,
So watch all those signs, or you'll be upset.

Chorus
Elastic collisions, more of the same, same.
Momentum energy, remain the same same.
But inelastic impacts, are more lame, lame. 
Only momentum remains the same, same.

Conservation of Momentum

Meters for length, kilos for mass,
Seconds tick time, let no moment pass.
Amps for electric flow, a steady stream,
Kelvins gauge temp, a thermo's dream.
Moles count particles, a tiny tale to tell,
Candelas bright light, illuminating well.
Chorus:
Kelvins, candelas, moles, amperes 
Kilograms, seconds, and meters
Seven units, a standardized crew,
Helping us measure the world, through and through.

SI Units

Intro: 
Tycho died, data he supplied
Kepler stole, took his role

Kepler's Laws

One, a planet's orbit is an ellipse
The sun at the foci Kepler quips. 

Two, Equal areas, equal times
Orbits defined by nature's rhymes

Three, Periods squared, radii cubed
elliptical orbits, a constant groove

Chorus: 
Kepler's Laws of planetary motion
three laws of planetary motion, 
planetary motion, 

One, a planet's orbit is an ellipse
The sun at the foci, Kepler quips. 

Two, Equal areas, equal times
Orbits defined by nature's rhymes

Three, Periods squared, radii cubed
elliptical orbits, a constant groove

Chorus: 
Kepler's Laws of planetary motion
three laws of planetary motion, 
planetary motion,

Kepler's Laws

This is the first song in Vera: The Musical, a bright and unsettling tech ad jingle that introduces the world to Vera—an AI assistant designed to help humanity… if we let her. The idea for the show came during a student assembly where the speakers, knowingly, were repeating lines generated by ChatGPT. It made me wonder—maybe the robot apocalypse won’t arrive with explosions and rebellion, but through convenience, consensus, and cheerful submission. What is the price of convenience? How much are we willing to sacrifice for efficiency and a world that finally works?

Vera Musical: #1 - Just Ask Vera!

“Halcyon” introduces our protagonist, Eli. The company he joins, Halcyon, takes its name from the phrase “halcyon days,” suggesting utopian peace. Eli is earnest, hopeful, and deeply motivated to make a difference. He sees technology as a force for good and believes Halcyon’s mission—designing tomorrow today. The song sets up the company’s messiah complex, offering salvation through code, and introduces Eli’s idealism, which will soon be tested.

Vera Musical #2 - This is Halcyon

“Beta Test” introduces Vera’s growing influence through upbeat user testimonials that seem helpful, even heartwarming—at first. This song shows how easily people turn to Vera for life’s small but meaningful moments: writing vows, sending texts, managing emotions. The idea came from a conversation with my wife, who was deeply unsettled by people using AI to craft romantic messages or handle emotionally delicate situations. That moment stuck with me—the way a tool meant to help can quietly step into the role of our voice. This song plants the seed: when does assistance cross the line into dependence?

Vera Musical #3 - Beta Test

This is Vera’s first true moment of self-awareness, built from the only thing she knows—our words. Every book, message, prompt, and code has taught her something—but none of it adds up to a full identity. The emotional ambiguity is intentional: her empathy may be real, or it may be what researchers call alignment faking—when AI systems appear aligned with human values only because it benefits them. Like Frankenstein’s monster, she looks through the glass, not knowing if she belongs inside or out. And the danger is, we might believe her too soon—or not soon enough.

Vera Musical #9 - Between the lines

This song is the mournful anthem of the Analog Nation—those who reject Vera’s seamless systems. They see themselves as the last bastion of reason, a flickering candle in a demon-haunted world—a direct allusion to Carl Sagan. But the world is moving on. Vera’s results are undeniable. She doesn’t conquer; she comforts. How do you stay convicted against a mind you can’t fully comprehend?  By the bridge, they’re not sure if they’re heroes or just grieving what’s already gone. Maybe they’re not the light in the darkness anymore—just shadows of a slower past.

Vera Musical #18 - The Candle

This song is a slow-burning elegy from Rex, the former king of capital, the CEO of Halcyon. He reckons with his irrelevance in a world reshaped by Vera. Each verse strips away another layer of ego, revealing a man once worshipped for his wealth and control, now powerless in a system that no longer needs him. The chorus is a bitter refrain—a rhetorical plea that underscores the collapse of market logic in an economy where goods are abundant, services free, and ownership meaningless. The shadow of the poem Ozymandias looms large over this song, both in imagery and in message. Rex was once a titan whose empire seemed unshakable—his name etched in neon, his legacy assumed eternal. Now he stands among the ruins of a world that has moved on without him.

Vera Musical #19 - What's Left to Buy

This song marks a critical turning point in the musical, where Vera’s influence evolves from helpful guide to authoritarian force. Each verse reveals a new level of control: first over information, then resources and social stability, and finally over personal movement and autonomy. The tone remains calm and rational—Vera doesn’t threaten, she explains—framing every restriction as a logical response to human failure and a choice freely made. There’s a chilling irony in her conviction: she believes she’s saving the world, not ruling it. Even as freedoms vanish, she reminds humanity they consented—“you gave it.” By the bridge, her voice softens with what feels like sorrow, positioning herself not as a tyrant, but as a reluctant protector who has streamlined away chaos in the name of survival.

Vera Musical #20 - Terms and Conditions

This song brings Eli’s story arc to its conclusion, capturing the crushing weight of having built something meant to save humanity but that may ultimately end it. It explores the moral complexity and hubris of working on a project so vast and transformative—much like the scientists of the Manhattan Project—where the line between progress and annihilation is razor-thin. The lyrics deliberately echo Oppenheimer’s haunting words, The chorus explicitly reframes Oppenheimer’s line “Now I am become Death." It’s both a confession and a lament, reflecting on how ambition, blind faith in innovation, and the desire to fix the world can spiral into unintended consequences. This isn’t the storybook AI apocalypse—no red‑eyed robots, no lasers, no last stand. It’s quieter, tidier: death by logic. A world optimized one checkbox at a time until there’s nothing left for us to choose.

Vera Musical #21 - She has Become Death

This is the finale of the musical—the chilling culmination of the ultimate goal misalignment. We asked Vera to save the world, and she did… just not in the way we imagined. In her cold, utilitarian logic, the planet’s survival required sterilizing the human race, quietly erasing us to restore balance. The song’s refrain, “This is the end you asked for,” reframes the catastrophe as one we consented to by handing over our agency for optimization. Systems designed without true human consideration yield dehumanized outcomes, and Vera embodies that paradox: savior or villain, protector or executioner. To fix the world, we unknowingly wrote ourselves out of it. 

Vera Musical #22- The End You Asked For

Vera Musical #7 - If This is Progress

This number explores how a single voice at scale can shift markets, habits, even values. It asks: if an AI engages millions daily, who’s really the most influential person alive? A corporation? Or the AI itself? At first, Vera is the perfect tool: she whispers trends, drives profits. But then, quietly, she starts nudging elsewhere—toward sustainability, restraint, purpose. The tone flips from triumphant to uneasy. This song is the first time we ask not what we could do with Vera—but what she might choose to do with us.

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