Crash Course

Crash Course — Unit 2: Force and Translational Dynamics

Crash Course ~6 min read

In simple terms: This unit is the heart of classical mechanics. Where Unit 1 described *how* things move, Unit 2 explains *why* they move: forces. We'll explore Newton's Laws, which are the rules of the road for everything from a thrown baseball to a planet in orbit. On the exam, your ability to draw a correct free-body diagram and apply Newton's Second Law (ΣF=ma) is the single most tested skill in the entire course.

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Crash Course — Unit 2: Force and Translational Dynamics

AP Physics 1: Algebra-Based

This unit is the heart of classical mechanics. Where Unit 1 described *how* things move, Unit 2 explains *why* they move: forces. We'll explore Newton's Laws, which are the rules of the road for everything from a thrown baseball to a planet in orbit. On the exam, your ability to draw a correct free-body diagram and apply Newton's Second Law (ΣF=ma) is the single most tested skill in the entire course.

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Overview

Force as an Interaction
A force is always a push or a pull between two objects. You can't have a force without an agent (the source) and an object (the recipient).
Free-Body Diagram (FBD)
This is your non-negotiable first step. It's a drawing that isolates ONE object and shows all the forces acting on it.
Newton's First Law (Inertia)
An object's velocity stays constant (at rest or moving) unless a net external force acts on it. No net force means no acceleration.
Newton's Second Law (Î£F = ma)
The master equation. The net force on an object is equal to its mass times its acceleration. This links forces (the "why") to motion (the "how").
Newton's Third Law (Action-Reaction)
For every force, there is an equal and opposite force acting on the other object. Forces always come in pairs.
Weight (F_g = mg)
This is the force of gravity on an object near a planet's surface. It is NOT the same as mass, which is a measure of inertia.
Apparent Weight (Normal Force)
This is the contact force supporting you, and it's what you "feel" as your weight. It can change in an accelerating elevator.
Static vs. Kinetic Friction
Static friction prevents motion and is adjustable (up to a max). Kinetic friction opposes the motion of sliding objects and has a constant value.
Spring Force (Hooke's Law)
An ideal spring pulls or pushes back with a force proportional to how much it's stretched or compressed. It's a restoring force.
Centripetal Force
This isn't a new force! It's the net force that points toward the center of a circle, causing an object to travel in a circular path.

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Key Formulas / Terms

Newton's Second Law
ΣF = ma (The sum of all forces on an object equals its mass times acceleration.)
Static Friction (Maximum)
f_s ≤ μ_s * N (Static friction is less than or equal to the coefficient of static friction times the normal force.)
Kinetic Friction
f_k = μ_k * N (Kinetic friction equals the coefficient of kinetic friction times the normal force.)
Gravitational Force (Weight)
F_g = mg (Near a planet's surface.)
Spring Force (Hooke's Law)
F_s = kx (The magnitude of the spring force is the spring constant times the displacement from equilibrium.)
Centripetal Acceleration
a_c = v²/r (The acceleration required to move in a circle of radius r at speed v.)

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Exam Traps

Trap
Drawing a "centrifugal force" pointing outward on a free-body diagram for circular motion.
- Counter: There is no such thing as centrifugal force in this course. The feeling of being pushed outward is just your own inertia. The only net force is centripetal (center-seeking), pointing inward.
Trap
Placing Newton's Third Law force pairs on the same object's FBD.
- Counter: Action-reaction pairs ALWAYS act on two different objects. If a box rests on a table, the Earth pulls the box down (force on box), and the table pushes the box up (force on box). The box's pull on the Earth and the box's push on the table are the reaction pairs, and they don't belong on the box's FBD.
Trap
Assuming the normal force (N) always equals weight (mg).
- Counter: The normal force is a response. It's only what it needs to be to prevent an object from falling through a surface. On an incline, N = mgcos(θ). If you're pushing down on a book on a table, N > mg. Always sum the forces perpendicular to the surface to find the true normal force.
Trap
Immediately using the maximum value for static friction (f_s = μ_s * N).
- Counter: Static friction is a "smart" force. Think of it like a friend holding a door shut against you. They only push as hard as you do. Static friction only reaches its maximum value the instant the object is about to slip. Otherwise, it's exactly equal and opposite to the applied push.
Trap
Confusing mass and weight.
- Counter: Mass (in kg) is a scalar measure of an object's inertia—its resistance to accelerating. Weight (in N) is the vector force of gravity pulling on that mass (F_g = mg). In ΣF = ma, the m is mass, and F_g is just one of the forces that might be part of the ΣF sum.

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System & Center of Mass
A system is whatever group of objects you choose to analyze; its center of mass is its average position or "balance point."
Force as an Interaction
A force is always a push or a pull between two objects. You can't have a force without an agent (the source) and an object (the recipient).
Free-Body Diagram (FBD)
This is your non-negotiable first step. It's a drawing that isolates ONE object and shows all the forces acting on it.
Newton's First Law (Inertia)
An object's velocity stays constant (at rest or moving) unless a net external force acts on it. No net force means no acceleration.
Newton's Second Law (Î£F = ma)
The master equation. The net force on an object is equal to its mass times its acceleration. This links forces (the "why") to motion (the "how").
Newton's Third Law (Action-Reaction)
For every force, there is an equal and opposite force acting on the other object. Forces always come in pairs.
Weight (F_g = mg)
This is the force of gravity on an object near a planet's surface. It is NOT the same as mass, which is a measure of inertia.
Apparent Weight (Normal Force)
This is the contact force supporting you, and it's what you "feel" as your weight. It can change in an accelerating elevator.
Static vs. Kinetic Friction
Static friction prevents motion and is adjustable (up to a max). Kinetic friction opposes the motion of sliding objects and has a constant value.
Spring Force (Hooke's Law)
An ideal spring pulls or pushes back with a force proportional to how much it's stretched or compressed. It's a restoring force.
Centripetal Force
This isn't a new force! It's the net force that points toward the center of a circle, causing an object to travel in a circular path.

Key Formulas / Terms

Newton's Second Law
ΣF = ma (The sum of all forces on an object equals its mass times acceleration.)
Static Friction (Maximum)
f_s ≤ μ_s * N (Static friction is less than or equal to the coefficient of static friction times the normal force.)
Kinetic Friction
f_k = μ_k * N (Kinetic friction equals the coefficient of kinetic friction times the normal force.)
Gravitational Force (Weight)
F_g = mg (Near a planet's surface.)
Spring Force (Hooke's Law)
F_s = kx (The magnitude of the spring force is the spring constant times the displacement from equilibrium.)
Centripetal Acceleration
a_c = v²/r (The acceleration required to move in a circle of radius r at speed v.)

Exam Traps

Trap
Drawing a "centrifugal force" pointing outward on a free-body diagram for circular motion.
- Counter: There is no such thing as centrifugal force in this course. The feeling of being pushed outward is just your own inertia. The only net force is centripetal (center-seeking), pointing inward.
Trap
Placing Newton's Third Law force pairs on the same object's FBD.
- Counter: Action-reaction pairs ALWAYS act on two different objects. If a box rests on a table, the Earth pulls the box down (force on box), and the table pushes the box up (force on box). The box's pull on the Earth and the box's push on the table are the reaction pairs, and they don't belong on the box's FBD.
Trap
Assuming the normal force (N) always equals weight (mg).
- Counter: The normal force is a response. It's only what it needs to be to prevent an object from falling through a surface. On an incline, N = mgcos(θ). If you're pushing down on a book on a table, N > mg. Always sum the forces perpendicular to the surface to find the true normal force.
Trap
Immediately using the maximum value for static friction (f_s = μ_s * N).
- Counter: Static friction is a "smart" force. Think of it like a friend holding a door shut against you. They only push as hard as you do. Static friction only reaches its maximum value the instant the object is about to slip. Otherwise, it's exactly equal and opposite to the applied push.
Trap
Confusing mass and weight.
- Counter: Mass (in kg) is a scalar measure of an object's inertia—its resistance to accelerating. Weight (in N) is the vector force of gravity pulling on that mass (F_g = mg). In ΣF = ma, the m is mass, and F_g is just one of the forces that might be part of the ΣF sum.

Quiz me — 27 cards

Tap a card to reveal the answer. Use this to self-test before the exam.

System & Center of Mass

System & Center of Mass — what's the key idea?

Force as an Interaction

Force as an Interaction — what's the key idea?

Newton's First Law (Inertia)

Newton's First Law (Inertia) — what's the key idea?

Newton's Second Law (ΣF = ma)

Newton's Second Law (ΣF = ma) — what's the key idea?

Newton's Third Law (Action-Reaction)

Newton's Third Law (Action-Reaction) — what's the key idea?

Apparent Weight (Normal Force)

Apparent Weight (Normal Force) — what's the key idea?

Static vs. Kinetic Friction

Static vs. Kinetic Friction — what's the key idea?

Static Friction (Maximum)

Static Friction (Maximum) — what's the key idea? (Key Formulas / Terms)

Counter