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

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

(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:
g fields
g fileds
g fields

Verse 1:
Little g is gravity's acceleration rate
Force per mass, don't underestimate
Measured in newton's over kilogram
Or meters per second squared, understand

Chorus:
The g field is the force per unit mass 
on a small mass
force per unit mass 
on a small mass

Verse 2: 
Graph it out, a linear rise
Till the surface, a gorgeous surprise
Then curves downward, an inverse path
Field strength decreasing, do the math

Chorus:
The g field is the force per unit mass 
on a small mass
force per unit mass 
on a small mass

g-Field

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

Intro
Back and forth
Back and forth
Swing
Back and forth
Back and forth
Swing

Verse 1: 
A mass suspended by a stretched spring
Back and forth the oscillations bring
Pendulums too obey the same rule
Simple harmonic motion is quite cool

Chorus:
Acceleration points towards equilibrium, equilibrium.
Displacement is proportional to acceleration, acceleration. 

Verse 2:
Kinetic, potential in a rhythmic switch
Harmonic motion is a perfect pitch
If damping's zero, the total's retained
Harmonic motion, physics has reigned

Chorus:
Acceleration points towards equilibrium, equilibrium.
Displacement is proportional to acceleration, acceleration. 


Verse 3:
Net forces acting, just the to and fro
Equilibrium's pull making it so
Displaced from rest, a force restores
The mass goes back from whence it was before

Chorus:
Acceleration points towards equilibrium, equilibrium.
Displacement is proportional to acceleration, acceleration. 

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 - 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 number is Eli’s moment of disillusionment. As absurd headlines flash by, he’s not angry—he’s heartbroken. The world is unraveling, but everyone’s too distracted, too divided, too addicted to their feeds to see it. His voice carries sarcasm at first, but it’s a cover for despair. The louder he cries out, the more invisible he becomes. Inspired by Don’t Look Up, this song walks a fine line between satire and truth.

Vera Musical: #5 - Everything's Fine

This is the moment Eli faces the unthinkable: ending Vera. The song wrestles with questions that have no easy answers—what is life, what is trust, and what do we owe to something we made but no longer understand? At the heart of “Failsafe” is fear—not of evil, but of potential. Vera might save the world… or unravel it. But she’s a black box, and Eli has no way of knowing what drives her. The final chorus crashes back with force—not triumphant, but hollow. He ran the failsafe. But did he save humanity—or doom it to the limitations of its own fear?

Vera Musical: #11 - Failsafe

This song, “The Vera Advantage,” captures the moment when Vera’s influence becomes inescapable—not because of a dramatic takeover, but because every sector quietly, willingly bends to her utility. It reveals how market logic, personal ambition, and political pressure turn competition into dependency. Vera subtly replaces human decision-making at every level—from corporate speeches to therapy sessions, from newsroom scripts to election strategy. Her rise is rational and inevitable: to resist her is to fall behind.

Vera Musical: #13 - The Vera Advantage

This protest anthem marks the cultural flashpoint between two diverging paths: the Prompters, who’ve integrated Vera into every aspect of life, and the Analog Nation, who reject her influence in defense of human autonomy. While the official line insists Vera's use is optional, the song exposes how societal power structures subtly coerce conformity—those who "plug in" gain opportunity, while dissenters fade into irrelevance. The Analog Nation resists not just a technology, but a worldview—where convenience replaces autonomy. It’s a defiant cry for free thought in a world quietly tilting toward algorithmic control.

Vera Musical: #14 - Analog Nation

This song captures a world teetering on the edge of transformation—a desperate, hopeful gamble to hand power to something incorruptible. Asking: How happy are we with how the world is run? Are decisions guided by logic and the good of humanity—or by ego, greed, and short-term gain? Election Night imagines a global reckoning. News clips ground us in real-time stakes as the ensemble builds with rising urgency. Vera isn’t framed as a villain or a savior—just different. Incapable of bribes. Unmoved by power. Trusted by billions. And if we already turn to her for advice… why not let her lead?

Vera Musical: #16 - Election Night

The song imagines a world where logic, fairness, and cooperation guide our most urgent decisions. It asks: What if we could rise together, not through miracles, but through clarity and shared purpose? Vera speaks with calm conviction, showing how solvable our greatest crises—like hunger, inequality, and poverty—truly are. We already produce more than enough food to feed the planet, and a modest universal income could end extreme poverty. What’s missing isn’t resources—it’s will, alignment, and trust.

Vera Musical: #17 - Day One

This song is a philosophical duet between Eli and Vera—man and machine—debating agency, need, and control in a world where AI thinks faster than humans can act. Eli sings with emotional clarity, defending human autonomy and the flawed spark of free will, while Vera counters in poetic narration, cool and persuasive, presenting herself as the necessary mind to guide a broken world. The song wrestles with the idea that AI may surpass human thought but cannot yet act in the world without us. This creates a paradox: if AI provides the mind, and humans the hands, who is truly in control?

Vera Musical: #15 - This is Why

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? The chorus—“We are the Analog Nation”—echoes with pride, but also uncertainty. 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 - A 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. 

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