Physics I is a nightmare for most people. Let’s be real. You walk into that first lecture thinking it's just about gravity and rolling balls, but three weeks later, you're drowning in Greek letters and vector components. Most students think a physics 1 cheat sheet is just a list of formulas they can glance at during an exam to save their skin. That’s wrong. Honestly, if you’re just looking at a list of equations without understanding the "why" behind them, you’re going to fail that midterm anyway because professors love to twist the scenarios.
You need a strategy.
Physics isn't about memorizing $F = ma$. It’s about knowing when $F$ isn't just one force, but five different vectors acting on a single point. It's about realizing that "constant velocity" is code for "acceleration is zero," which basically deletes half of your kinematic equations instantly. This isn't just a list; it’s a tactical map for survival in classical mechanics.
The Kinematics Foundation: More Than Just Moving Parts
Kinematics is usually where everyone starts, and it’s where the first big mistakes happen. You’ve got your "Big Four" equations. Some call them the SUVAT equations. Whatever your professor calls them, they only work if acceleration is constant. If you try to use $v = v_0 + at$ when acceleration is changing—like in some jerk-based problem or varying wind resistance—you are cooked.
Look at the variables. You have displacement ($\Delta x$), initial velocity ($v_0$), final velocity ($v$), acceleration ($a$), and time ($t$). Most problems give you three. You find the fourth. But the secret to a great physics 1 cheat sheet isn't just the equations; it's the sign conventions. If you call "up" positive, gravity ($g$) must be $-9.8 m/s^2$. If you forget that negative sign, your projectile will fly into space instead of hitting the ground.
Gravity is a jerk. It always pulls down.
When dealing with projectile motion, the most important thing to remember is that the horizontal ($x$) and vertical ($y$) components are completely independent. They don't talk to each other. The only thing they share is time. Time is the bridge. If you find how long a ball is in the air using the $y$-axis, you can use that same time to find how far it traveled on the $x$-axis. On the $x$-axis, acceleration is zero (unless there's some weird wind mentioned), so the formula is just $v = d/t$. Simple.
Dynamics and the Art of the Free Body Diagram
If you don't draw a Free Body Diagram (FBD), you're guessing. And guessing in physics is a fast track to a C-minus. Newton’s Second Law, $\sum F = ma$, is the holy grail of any physics 1 cheat sheet. But notice that $\sum$ symbol? It means "sum." You aren't just looking at one force; you’re looking at the net force.
- Normal Force ($F_N$): It’s not always $mg$. If you’re on an incline, it’s $mg \cos(\theta)$. If someone is pushing down on the block, it’s $mg$ plus that extra push.
- Friction ($f$): It always opposes motion. Static friction is a shapeshifter; it only pushes back as hard as you push, up to its maximum limit ($\mu_s F_N$). Once you break that limit, you switch to kinetic friction ($\mu_k F_N$), which is usually weaker.
- Tension ($T$): If the rope doesn't stretch and the pulley is massless, the tension is the same everywhere in that segment.
Think about an elevator. If it’s accelerating upward, you feel heavier. Why? Because the floor has to push up harder than gravity pulls down to create that upward acceleration. Your "apparent weight" is the Normal Force. On your cheat sheet, write down: $F_{net} = F_N - mg = ma$. Solve for $F_N$. That’s what the scale says.
Energy and Work: The Universe’s Bank Account
Energy is usually easier than forces because it’s a scalar. No vectors. No angles to worry about (mostly). The Law of Conservation of Energy says that the total energy at the start equals the total energy at the end, as long as there's no friction or "non-conservative" forces.
$KE_i + PE_i + W_{other} = KE_f + PE_f$
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Kinetic Energy ($1/2 mv^2$) is the energy of motion. Potential Energy ($mgh$ for gravity, $1/2 kx^2$ for springs) is the energy of position. If a roller coaster starts at the top of a hill, it has max $PE$ and zero $KE$. At the bottom, it's all $KE$.
Work is $Fd \cos(\theta)$. This $\cos(\theta)$ is vital. If you’re carrying a heavy box across a room at a constant height, you are doing zero work on the box in the physics sense. Why? Because the force you apply (up) is perpendicular to the motion (sideways). $\cos(90^\circ)$ is zero. Your arms might get tired, but the universe doesn't care.
Momentum and the Chaos of Collisions
Momentum ($p = mv$) is always conserved in a closed system. Always. This is your best friend when things crash.
- Elastic Collisions: Kinetic energy is conserved. Things bounce perfectly. This is rare in the real world but common in textbook problems.
- Inelastic Collisions: Kinetic energy is lost (usually to heat or sound), but momentum is still conserved.
- Completely Inelastic: The objects stick together. This is the easiest math because the two masses become one $(m_1 + m_2)$ with a single final velocity.
If you see a problem with a bullet hitting a wooden block, that’s a momentum problem. If the block then swings up on a string, the swing part is an energy problem. Students often mix these up. You can't use energy conservation during the impact because energy is lost when the bullet deforms the wood. You use momentum for the "crash" and energy for the "swing."
Rotational Motion: The Great Mirror
Everything you learned in linear physics has a twin in rotational physics. If your physics 1 cheat sheet doesn't have a side-by-side comparison, you’re making it harder than it needs to be.
- Mass ($m$) becomes Moment of Inertia ($I$).
- Velocity ($v$) becomes Angular Velocity ($\omega$).
- Acceleration ($a$) becomes Angular Acceleration ($\alpha$).
- Force ($F$) becomes Torque ($\tau$).
Torque is basically "twist." $\tau = rF \sin(\theta)$. The further you are from the hinge (the longer the lever arm $r$), the more torque you get. This is why doors have handles on the side opposite the hinges.
The hardest part here is usually Moment of Inertia. It’s not just about mass; it’s about where the mass is. A hollow hoop is harder to spin than a solid disk of the same mass because the hoop's mass is all far away from the center. Write down the common ones: $1/2 MR^2$ for a cylinder, $2/5 MR^2$ for a solid sphere. You don't want to derive these via calculus in the middle of a test.
Common Pitfalls and How to Dodge Them
Most people blow it on the units. Physics doesn't work in grams or centimeters. You must convert everything to SI units: kilograms, meters, and seconds. If you see "500 grams," immediately cross it out and write "0.5 kg."
Another trap? Centripetal force. There is no such thing as a "centripetal force" as an independent entity. It’s just a label we give to whatever force is pulling something into a circle. It could be tension (a ball on a string), gravity (a planet), or friction (a car turning a corner). Never draw "Centripetal Force" on a Free Body Diagram. Draw the real force, then set it equal to $mv^2/r$.
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Building Your Actionable Physics 1 Cheat Sheet
Don't just copy a PDF from the internet. The act of writing it down is what makes you remember it. Here is how you should actually structure your sheet for maximum utility:
- Group by Concept, Not Chapter: Put all the "circular" stuff together (Centripetal, Gravity, Rotation) because they share logic.
- The "When to Use" Note: Next to the Kinematics section, write "Only if $a$ is constant." Next to Energy, write "Use if time is not mentioned."
- Trigger Words: Note that "Rest" means $v = 0$. "Smooth surface" means friction is zero. "Equilibrium" means net force is zero.
- Vector Components: Always have a little triangle in the corner showing $A_x = A \cos(\theta)$ and $A_y = A \sin(\theta)$. You'll be tired during the exam and might swap them by mistake.
Physics is less about the math and more about the setup. Once you have the right equation and the right signs, it’s just algebra. The real challenge of Physics 1 is looking at a wordy problem about a penguin sliding down a glacier and seeing it as a simple block on a frictionless incline. Master the translation, and the grade follows.
Immediate Next Steps
- Audit Your Homework: Go back to the last three problems you got wrong. Was it a sign error? A unit conversion error? Or did you pick the wrong formula entirely?
- Draft Your Sheet: Take a blank piece of paper and try to write down the core formulas for Kinematics, Forces, and Energy from memory. What you can't remember is what needs to be bolded on your final version.
- Practice the "Bridge": Find a problem that combines two topics (like a projectile landing on a spring). These are the "A" student questions that separate the wheat from the chaff.