Ultimate Knowt Guide: AP Physics C, 2023

Vectors

These specify the magnitude and direction.

Scalars

These specify the magnitude and no direction.

Speed

indicates how fast an object is moving but not in what direction.

Velocity

indicates both how fast an object is moving and in what direction.

Speed

Indicates how fast an object is moving but not in what direction.

Vector Addition

Vector Subtraction

Scalar Multiplication

perpendicular

If two vectors are \________ , their dot product will equal zero [cos(π/2) \= 0].

parallel

If two vectors are \_______ , their dot product will equal the product of their magnitudes (cos 0 \= 1).

antiparallel

If two vectors are \_________ , their dot product will be the negative of the product of their magnitudes [cos(π) \= −1].

Scalar Product

Dot product is also known as?

third

The cross product of two vectors yields a \____ vector.

Vector Product

Cross product is also known as?

units

All measurements and observable quantities have \________; otherwise they would be meaningless.

Velocity

Indicates both how fast an object is moving and in what direction.

Instantaneous velocity (2D Kinematics)

Instantaneous speed

The magnitude of instantaneous velocity.

Instantaneous speed (2D Kinematics)

Instantaneous acceleration (2D Kinematics)

Displacement

The net difference in the location of an object independent of how the object got there.

Average quantities

These are often denoted as the variable with a bar over it (v, a)

Derivation of Average Velocity

Derivation of Average Speed

Total Distance

The distance traveled irrespective of direction

vectors

Velocities and displacements are \__________

scalars

speeds and distances are \_________

Derivation of Average Acceleration

fundamental schematic

positive curvature

Positive acceleration corresponds to \____________

negative curvature

Negative acceleration corresponds to \_________

position vector

A natural way to describe the position of an object in more than one dimension is to define a \_______ that points from the origin to the location of the object.

Position Vector Definiton

Instantaneous velocity (2D Kinematics)

Instantaneous speed (2D Kinematics)

Instantaneous acceleration (2D Kinematics)

two-dimensional vector equations

The definitions of velocity and acceleration are \____________ , each of which is equivalent to a set of two one-dimensional equations.

definition of velocity

instantaneous velocity

For the \______________ vector , the magnitude is the speed (a scalar), and its direction is in the direction of motion (tangent to the path of the object).

Vector addition relates the position of an object relative to two different frames of reference

Tangential Acceleration (a∥)

Affects only the magnitude of the velocity vector.

Radial Acceleration  (a⊥)

Affects only the direction of the velocity vector.

ω

determines the sense of rotation

magnitude of ω

determines how quickly the r(t) vector rotates.

Phase shift angle (ϕ)

A parameter that determines the initial angle and thus the initial position.

Nonuniform circular motion

Refers to motion in a circular path with nonconstant velocity.

Newton’s First Law

When the net force acting on a body is zero, its acceleration must be zero, meaning that the velocity remains constant.

Newton’s First Law

Superposition of Forces

Inertia

It refers to how much an object resists a change in its velocity and is measured by mass.

Newton’s Second Law

This law reveals that force is a vector parallel to the acceleration.

Newton’s Second Law

pounds or newtons

Force is measured in \____________.

Newton’s Third law

For every force exerted by one object on another, there is another force equal in magnitude and opposite in direction that is exerted back by the second object on the first.

Mass

A measure of inertia and is the proportionality constant that relates force to acceleration in Newton’s second law.

Kilograms

SI Unit of Mass

Weight

The magnitude of the force exerted on an object by the closest nearby planet (typically Earth) according to the formula.

Gravitational Force

The most prevalent force in the universe, pulling together on any two objects with mass in the universe.

Normal Force

Denotes FN. Its magnitude is determined by Newton’s second law. Always perpendicular.

Frictional Force

Force that resists the sliding or rolling of one solid object over another.

Static Friction

Objects are not sliding relative to each other.

Static Friction

Kinetic Friction

Kinetic Friction

Objects are sliding relative to each other.

Tension Force

A force that develops in a rope, thread, or cable as it is stretched under an applied force.

Static equilibrium (object at rest)

Weight formula

Work by One Force

Work due to multiple forces

Work due to multiple forces expanded

Joule

The unit of work and energy

Work

the change in an object’s kinetic energy due to the action of a given force.

Work–kinetic energy theorem

Work–kinetic energy theorem

This is the first and most fundamental of a number of equations we will soon derive relating various types of work and energy. This theorem is a restatement of Newton’s laws, and it is always valid.

Energy

never created or destroyed; it merely changes form.

Conservative forces

Are involved in reversible energy conversions, where we can get our kinetic energy back.

Nonconservative forces

Are involved in irreversible energy conversions; though the total energy is always conserved, energy is converted to forms from which we cannot recover

Conservative forces

kinetic energy ⇒ potential energy ⇒ kinetic energy

Nonconservative forces

kinetic energy ⇒ sound, heat, etc. ⇒ cannot be easily recovered

General definition of a potential energy function

Gravitational potential energy

Work done by gravitational force

spring constant

The proportionality constant k , called the \_____________ or force constant, is a property of the particular spring.

restoring force

Because the force always tries to restore the spring to its relaxed state, whether it has been stretched or compressed, it is called a \_______________ .

Elastic Potential Energy

Work Done by Spring Force

general form of the energy conservation equation

Power

The rate at which a force does work on a system

Average power

Constant power

Watt

Unit of power

Turning Points

All the energy is potential energy, so the object is temporarily at rest.

Equilibrium Points

Points at which the force is zero

Stable equilibrium points

Points where, if the object is given a small nudge, it will remain close to the equilibrium point, oscillating within an “energy well”.

Unstable equilibrium points

Points where, if the object is given a small displacement, it will end up far away from the equilibrium point

Neutral equilibrium points

Points where the U(x) curve is completely flat, so if the particle is given a little nudge, it will continue to move with a constant velocity.

Momentum

Momentum

It obeys superposition such that the net momentum of a collection of objects is the vector sum of the momentum of each object

Linear momentum

A vector parallel to velocity

Relationship Between Force and Momentum