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UPCAT PhysicsNewton'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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