UPCAT Physics — Newton's Laws, Dynamics & MomentumCheat Sheet
Cheat sheet for UPCAT Physics — Newton's Laws, Dynamics & Momentum. Compact, printable, and organised around the concepts University of the Philippines tests most frequently in the UPCAT 2026. Perfect for the week before exam day.
Exam context
On the UPCAT 2026, the Physics subtest carries a "Core" weight in University of the Philippines's pattern. Newton's Laws, Dynamics & Momentum lands at position 3rd out of 6 in the standard review order. Target score is UPG ≤ 2.2 typical, and roughly 20 items come from Physics on a typical UPCAT paper.
Newton's Laws, Dynamics & Momentum - Cheat sheet
Your last-minute revision companion for Newton's Laws, Dynamics & Momentum - everything you need for UPCAT Physics
Sections
Formulas
Formula
ΣF = 0 (First Law)
Meaning
ΣF = sum of all forces acting on object
Watch Out
Only applies when acceleration = 0
When To Use
Object at rest or moving at constant velocity
Formula
F = ma (Second Law)
Meaning
F = net force (N), m = mass (kg), a = acceleration (m/s²)
Watch Out
Use NET force, not individual forces
When To Use
Any problem involving force and acceleration
Formula
F₁₂ = -F₂₁ (Third Law)
Meaning
F₁₂ = force of object 1 on 2, F₂₁ = force of object 2 on 1
Watch Out
Forces act on DIFFERENT objects, never cancel each other
When To Use
Action-reaction force pairs
Common Values
Value
9.8 m/s²
Symbol
g
Quantity
Gravitational acceleration (Earth)
Section Title
Newton's Three Laws
Important Facts
- First Law is also called Law of Inertia
- Mass is measure of inertia
- Newton (N) = kg⋅m/s²
- Weight = mg, where g = 9.8 m/s² on Earth
- Action-reaction pairs never act on same object
- Zero net force means zero acceleration (not zero velocity)
Key Definitions
Term
Force
Example
Weight = mg downward
Definition
A push or pull that causes acceleration; vector quantity
Term
Inertia
Example
Heavier objects harder to push
Definition
Tendency of objects to resist changes in motion
Term
Net Force
Example
If 10N right and 6N left, net = 4N right
Definition
Vector sum of all forces acting on an object
Diagrams To Know
- Free body diagrams showing all forces
- Action-reaction force pairs on different objects
- Force vectors and their components
Formulas
Formula
Fg = mg
Meaning
Fg = gravitational force/weight (N), m = mass (kg), g = 9.8 m/s²
Watch Out
Weight varies with gravity; mass stays constant
When To Use
Finding weight of objects
Formula
Fs = μsN (Static Friction)
Meaning
Fs = max static friction (N), μs = coefficient static friction, N = normal force (N)
Watch Out
Static friction ≤ μsN, not always equal
When To Use
Object about to move but still stationary
Formula
Fk = μkN (Kinetic Friction)
Meaning
Fk = kinetic friction (N), μk = coefficient kinetic friction, N = normal force (N)
Watch Out
μk < μs always; kinetic friction is constant
When To Use
Object already sliding/moving
Formula
Fspring = -kx
Meaning
Fspring = spring force (N), k = spring constant (N/m), x = displacement (m)
Watch Out
Negative sign means force opposes displacement
When To Use
Springs compressed or stretched
Common Values
Value
μs = 0.6-1.0, μk = 0.4-0.8
Symbol
μ
Quantity
Coefficient of friction (typical values)
Section Title
Types of Forces
Important Facts
- Normal force ≠ weight on inclined planes
- Friction always opposes motion
- Static friction can vary from 0 to maximum value
- Kinetic friction is constant while sliding
- Air resistance increases with speed
- Spring force follows Hooke's Law
Key Definitions
Term
Normal Force
Example
Table pushing up on book
Definition
Contact force perpendicular to surface
Term
Tension
Example
String pulling object upward
Definition
Force transmitted through rope, string, or cable
Term
Applied Force
Example
Pushing a box across floor
Definition
External force applied by person or object
Diagrams To Know
- Inclined plane with force components
- Friction force directions
- Spring force vs displacement graph
Formulas
Formula
W = F⋅d⋅cos(θ)
Meaning
W = work (J), F = force (N), d = displacement (m), θ = angle between F and d
Watch Out
Use parallel component of force only
When To Use
Calculating work done by force
Formula
P = W/t
Meaning
P = power (W), W = work (J), t = time (s)
Watch Out
1 Watt = 1 J/s; 1 hp = 746 W
When To Use
Finding rate of work done
Formula
P = F⋅v
Meaning
P = power (W), F = parallel force (N), v = velocity (m/s)
Watch Out
Use component of force parallel to velocity
When To Use
Power during constant velocity motion
Formula
KE = ½mv²
Meaning
KE = kinetic energy (J), m = mass (kg), v = velocity (m/s)
Watch Out
Velocity is squared - doubling v gives 4× energy
When To Use
Energy due to motion
Formula
PE = mgh
Meaning
PE = gravitational potential energy (J), m = mass (kg), g = 9.8 m/s², h = height (m)
Watch Out
Height is relative to chosen reference point
When To Use
Energy due to position in gravitational field
Section Title
Work, Energy & Power
Important Facts
- Work = 0 when force ⟂ displacement (cos 90° = 0)
- Negative work removes energy from system
- Joule (J) = N⋅m = kg⋅m²/s²
- Power measured in Watts (W) or horsepower (hp)
- Conservative forces allow energy conservation
- Work-Energy Theorem: Wnet = ΔKE
Key Definitions
Term
Work
Example
Lifting box does positive work against gravity
Definition
Energy transferred by force causing displacement
Term
Power
Example
Motor with higher power lifts objects faster
Definition
Rate at which work is done or energy is transferred
Term
Conservative Force
Example
Gravity, spring force
Definition
Force where work depends only on start/end points
Diagrams To Know
- Work calculation with force at angle
- Energy bar charts showing KE and PE changes
- Power vs time graphs
Reactions Or Equations
Note
Mechanical energy conservation
Equation
Emech = KE + PE = constant
Conditions
No friction or air resistance (conservative system)
Formulas
Formula
p = mv
Meaning
p = momentum (kg⋅m/s), m = mass (kg), v = velocity (m/s)
Watch Out
Momentum is vector - direction matters
When To Use
Finding momentum of moving object
Formula
Σpi = Σpf (Conservation)
Meaning
Σpi = total initial momentum, Σpf = total final momentum
Watch Out
Must use vector addition for 2D problems
When To Use
Collisions and explosions with no external forces
Formula
J = Ft = Δp
Meaning
J = impulse (N⋅s), F = average force (N), t = time (s), Δp = change in momentum
Watch Out
Impulse equals change in momentum
When To Use
Force acting over time interval
Formula
mAvA + mBvB = (mA + mB)v' (Inelastic)
Meaning
Objects stick together after collision, v' = final common velocity
Watch Out
Kinetic energy is not conserved
When To Use
Perfectly inelastic collisions
Formula
mAvA + mBvB = mAv'A + mBv'B (Elastic)
Meaning
Objects bounce apart after collision
Watch Out
Both momentum and kinetic energy conserved
When To Use
Perfectly elastic collisions
Section Title
Momentum & Collisions
Important Facts
- Momentum conserved in all collisions (if no external forces)
- Kinetic energy conserved only in elastic collisions
- Impulse = area under F vs t graph
- Longer collision time means smaller force
- In elastic collision, relative velocity reverses
- System momentum = vector sum of individual momenta
Key Definitions
Term
Momentum
Example
Truck has more momentum than car at same speed
Definition
Product of mass and velocity; measure of motion quantity
Term
Impulse
Example
Airbag increases collision time, reduces force
Definition
Product of force and time; equals change in momentum
Term
Collision
Example
Billiard balls hitting each other
Definition
Event where objects exert forces on each other over short time
Diagrams To Know
- Before/after diagrams for collisions
- Force vs time graphs showing impulse
- Momentum vector diagrams for 2D collisions
Reactions Or Equations
Note
Impulse-momentum theorem
Equation
FΔt = mΔv
Conditions
Constant force over time interval
Formulas
Formula
ΣFx = max, ΣFy = may
Meaning
Apply F = ma in x and y directions separately
Watch Out
Components must be in same coordinate system
When To Use
2D force problems with acceleration
Formula
N = mg cos(θ) (Incline)
Meaning
N = normal force, θ = angle of incline from horizontal
Watch Out
θ is measured from horizontal, not from normal
When To Use
Objects on inclined planes
Formula
mg sin(θ) (Down incline)
Meaning
Component of weight parallel to inclined surface
Watch Out
This is net force if no friction
When To Use
Force causing acceleration down incline
Section Title
Dynamics Problem Solving
Important Facts
- Always draw free body diagram first
- Include only forces ON the object, not BY the object
- Choose coordinate system before resolving forces
- On inclines: parallel and perpendicular to surface
- Tension same throughout massless rope
- Connected objects have same acceleration magnitude
Key Definitions
Term
Free Body Diagram
Example
Box on table: weight down, normal up, applied right, friction left
Definition
Diagram showing all forces acting on single object
Term
Equilibrium
Example
Book on table or car at constant speed
Definition
State where net force is zero (static or constant velocity)
Diagrams To Know
- Free body diagrams for various situations
- Force resolution into components
- Pulley systems with tension forces
Must Remember
- F = ma is for NET force only, not individual forces
- Action-reaction pairs act on DIFFERENT objects
- Weight = mg (force), mass stays constant everywhere
- Work = 0 when force perpendicular to displacement
- Power = Work/time = Force × velocity (parallel component)
- Momentum = mv is conserved in all collisions
- Impulse = FΔt = Δp (change in momentum)
- On inclines: N = mg cos θ, parallel component = mg sin θ
- Static friction ≤ μsN, kinetic friction = μkN (constant)
- Energy conserved only if no friction/air resistance
Last Minute Tips
- Draw free body diagrams before writing equations - saves time and prevents errors
- For inclines, always resolve weight into parallel and perpendicular components first
- In collision problems, set up momentum conservation equation immediately
- Check units: Force (N), Work/Energy (J), Power (W), Momentum (kg⋅m/s)
- For Newton's 3rd Law questions, identify which object exerts force on which
Comparison Tables
Rows
Values
- Object at rest or about to move
- Object already sliding
Property
When it acts
Values
- Fs ≤ μsN
- Fk = μkN
Property
Formula
Values
- μs (larger)
- μk (smaller)
Property
Coefficient value
Values
- Variable (0 to maximum)
- Constant while sliding
Property
Force magnitude
Columns
- Property
- Static Friction
- Kinetic Friction
Table Title
Static vs Kinetic Friction
Rows
Values
- Yes
- Yes
Property
Momentum conserved
Values
- Yes
- No
Property
Kinetic energy conserved
Values
- Bounce apart
- May stick together
Property
Objects after collision
Values
- Billiard balls, atoms
- Car crashes, clay balls
Property
Real examples
Columns
- Property
- Elastic
- Inelastic
Table Title
Elastic vs Inelastic Collisions
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