What does this Physics I: Mechanics cheat sheet cover?

It has 11 sections: Kinematics, Projectile Motion, Newton's Laws, Friction, Circular Motion, Work Energy, Energy Conservation, Momentum, Rotation, Inertia Angular Momentum and SHM Gravitation. Together they cover the topics a typical Physics I: Mechanics exam tests, including kinematics equations, projectile motion, Newton's laws and free-body diagrams and friction.

Is the physics formula sheet: mechanics free?

The first part is free to read on this page, with no account needed. The full sheet opens in the app with Unlimited ($4.99 a month or $19 for a semester), where you can edit it, print it or save it as a PDF. It is one US Letter page and prints cleanly in black and white or colour.

Can I bring this Physics I: Mechanics cheat sheet to my exam?

Only if your course allows a note sheet, so check the syllabus. This one is a single US Letter page. If your exam allows a different size, such as a 3x5 or 4x6 index card or one page front and back, Cheat Sheet AI makes one at exactly that size from your own lecture notes.

The sheet was written by our engine from a standard course outline, then a second model fact-checked every formula and statement against it; it made no corrections before publishing. Notation and emphasis vary between courses, so check it against your own lecture notes.

Can I make a Physics I: Mechanics sheet from my own notes?

Yes. Upload your lecture slides, notes or study guide and Cheat Sheet AI writes a sheet in your course's notation, sized to exactly the space your exam allows. Your first sheets are free.

Physics & EngineeringPhysics I: Mechanics

Physics Formula Sheet: Mechanics — 1-page PDF

Core formulas, definitions, and procedures for kinematics through gravitation. The whole course on one dense, printable page for your midterm or final, with every formula typeset and worked examples where they help.

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For a specific exam: Physics I Midterm 1 study sheet, Physics I Final exam study sheet.

1 pageUS Letter
11 sections12 topics
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Preview of the one-page Physics I: Mechanics cheat sheet: Core formulas, definitions, and procedures for kinematics through gravitation — the whole course, one page

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What’s on it

The topics a typical Physics I: Mechanics exam tests, all on the one page.

Kinematics equations
Projectile motion
Newton's laws and free-body diagrams
Friction
Circular motion
Work, energy, power
Conservation of energy
Momentum and collisions
Rotational kinematics and torque
Moment of inertia and angular momentum
Simple harmonic motion
Gravitation

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The free part, as text

The free part of the sheet, section by section. Unlock the full sheet to read the rest, edit any block, and print it or save it as a PDF.

01Kinematics

Position / displacement: Position $x (t)$ ; displacement $Δ x = x_{f} - x_{i}$ .

Average velocity

v_{avg} = \frac{Δ x}{Δ t}

1D motion; signed quantity.

Average speed

speed_{avg} = \frac{total distance}{Δ t}

Scalar.

Instantaneous velocity

v = \frac{d x}{d t}

Slope of $x$ vs. $t$ .

Instantaneous acceleration

a = \frac{d v}{d t} = \frac{d ^{2} x}{d t ^{2}}

Slope of $v$ vs. $t$ .

Const- $a$ equations

v = v_{0} + a t x = x_{0} + v_{0} t + \frac{1}{2} a t^{2} v^{2} = v_{0}^{2} + 2 a (x - x_{0}) x - x_{0} = \frac{1}{2} (v_{0} + v) t

Valid only for constant acceleration in 1D.

Ex.Given $v_{0} = 2$ m/s, $a = 3$ m/s $^{2}$ , $t = 4$ s, find $v$ and $Δ x$ .

$v = 2 + 3 (4) = 14$ m/s; $Δ x = 2 (4) + \frac{1}{2} 3 (4^{2}) = 8 + 24 = 32$ m.

02Projectile Motion

Components

x = x_{0} + v_{0 x} t y = y_{0} + v_{0 y} t - \frac{1}{2} g t^{2}

No air resistance; $a_{x} = 0$ , $a_{y} = - g$ .

03Newton's Laws

Draw object isolated.
Choose axes; resolve angled forces.
Write $\sum F_{x} = m a_{x}$ , $\sum F_{y} = m a_{y}$ (and $\sum F_{z} = m a_{z}$ if needed).
Solve algebraically before plugging numbers.

Incline setupBlock on incline angle $θ$ ; weight $m g$ .

Choose axes parallel/perpendicular to plane. Components: $m g sin θ$ down slope, $m g cos θ$ into plane.

04Friction

Static friction

f_{s} \leq μ_{s} N

Adjusts as needed up to max $μ_{s} N$ .

Kinetic friction

f_{k} = μ_{k} N

Opposes relative sliding.

Normal force: Contact force perpendicular to surface; not always equal to $m g$ .

Common directions

Situation	Friction direction
Object tends to slide right	Left
Object slides left	Right
No relative motion	Opposes impending motion

Watch out:Static friction is not always $μ_{s} N$ ; only at threshold of slipping. In equilibrium, $f_{s}$ may be smaller.

05Work Energy

Potential energy

U_{g} = m g h U_{s} = \frac{1}{2} k x^{2}

Near Earth; spring about equilibrium.

Conservative force

W_{c} = - Δ U

Path independent; closed-loop work $= 0$ .

WorkForce $10$ N at $3 0^{\circ}$ to displacement $5$ m. Work?

$W = F d cos θ = 10 \cdot 5 \cdot cos 3 0^{\circ} = 253 \approx 43.3$ J.

06Energy Conservation

Mechanical energy

E_{mech} = K + U

Use when only conservative forces do work.

Conservation

K_{i} + U_{i} = K_{f} + U_{f}

If no nonconservative work.

With nonconservative work

K_{i} + U_{i} + W_{nc} = K_{f} + U_{f}

$W_{nc}$ = work by friction/external nonconservative forces.

Spring energy

U_{s} = \frac{1}{2} k x^{2}

Zero at equilibrium; $x$ from equilibrium.

Watch out:Potential energy zero level is arbitrary; only differences matter.

07Rotation

Torque

τ = r \times F ∣ τ ∣ = r F sin ϕ

About chosen axis.

Rotational dynamics

\sum τ = I α

About fixed axis.

Watch out:Use radians for $θ$ in rotation formulas; $s = r θ$ fails in degrees.

08Inertia Angular Momentum

Moment of inertia

I = \sum m r^{2} (or I = \int r^{2} d m)

Depends on axis.

Common $I$

Object	Axis
Hoop	$I = M R^{2}$
Solid disk/cylinder	$I = \frac{1}{2} M R^{2}$
Solid sphere	$I = \frac{2}{5} M R^{2}$
Rod center	$I = \frac{1}{12} M L^{2}$
Rod end	$I = \frac{1}{3} M L^{2}$

Parallel-axis

I = I_{cm} + M d^{2}

Axis shifted by distance $d$ .

Rotational KE

K_{rot} = \frac{1}{2} I ω^{2}

For rigid body about fixed axis.

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Also on the full Physics I: Mechanics sheet

10 more sections, with every definition, formula and worked example. Unlimited unlocks every full sheet in the library to edit, print or save as a PDF, and makes unlimited sheets from your own notes.

Projectile Motion

Velocity components
Launch speed
Range
Time of flight
Max height

Newton's Laws

Newton 1
Newton 2
Newton 3
Free-body diagram

Friction

Circular Motion

Centripetal acceleration
Centripetal force
Angular speed
Period / frequency

Work Energy

Work
Kinetic energy
Work-energy theorem
Power

Energy Conservation

Momentum

Momentum
Impulse
Conservation of momentum
Elastic collision
Perfectly inelastic

Rotation

Angular variables
Const-α equations
Arc length
Tangential accel

Inertia Angular Momentum

Angular momentum
Angular impulse / conservation

SHM Gravitation

Hooke's law
SHM equation
Period mass-spring
Period pendulum
SHM energy
Newton gravitation
Grav. field / potential
Circular orbit

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Questions

About the Physics I: Mechanics sheet and making your own.

What does this Physics I: Mechanics cheat sheet cover?: It has 11 sections: Kinematics, Projectile Motion, Newton's Laws, Friction, Circular Motion, Work Energy, Energy Conservation, Momentum, Rotation, Inertia Angular Momentum and SHM Gravitation. Together they cover the topics a typical Physics I: Mechanics exam tests, including kinematics equations, projectile motion, Newton's laws and free-body diagrams and friction.
Is the physics formula sheet: mechanics free?: The first part is free to read on this page, with no account needed. The full sheet opens in the app with Unlimited ($4.99 a month or $19 for a semester), where you can edit it, print it or save it as a PDF. It is one US Letter page and prints cleanly in black and white or colour.
Can I bring this Physics I: Mechanics cheat sheet to my exam?: Only if your course allows a note sheet, so check the syllabus. This one is a single US Letter page. If your exam allows a different size, such as a 3x5 or 4x6 index card or one page front and back, Cheat Sheet AI makes one at exactly that size from your own lecture notes.
How accurate is it?: The sheet was written by our engine from a standard course outline, then a second model fact-checked every formula and statement against it; it made no corrections before publishing. Notation and emphasis vary between courses, so check it against your own lecture notes.
Can I make a Physics I: Mechanics sheet from my own notes?: Yes. Upload your lecture slides, notes or study guide and Cheat Sheet AI writes a sheet in your course's notation, sized to exactly the space your exam allows. Your first sheets are free.

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