AP Physics 1 ALL UNITS

Units 1-8

Vector

A quantity described by both magnitude and direction

What are the conventional positive and negative directions for vectors?

Positive is north or east. Negative is south or west.

Examples of vector quantities

Position, displacement, velocity, acceleration

Scalar

A quantity described by magnitude only that will always be positive

Examples of scalar quantities

Mass, distance, speed, volume, temperature, energy

Describe how vectors can be modeled as arrows

The length represents magnitude and the direction represents the vector’s direction

What is the tail of a vector arrow?

The straight line of an arrow, whose length represents magnitude

What is the tip of a vector arrow?

The head of an arrow, whose direction represents the vector’s direction

How do vector directions correspond to signs?

Opposite directions = opposite signs

Vector notation options

1. Vectors can be noted with an arrow above the variable symbol

2. Vector notation is not necessary when you specify an axis, like x or y, with a subscript

How to add vectors visually

Align the tip of one arrow with the tail of the second. The vector sum is the arrow from the tail of the first to the tip of the second.

How to add vectors algebraically

Length = sqrt (X²+Y²)

Direction = tan^-1(Y/X)

How to subtract vectors visually

Make one vector negative by keeping its length and changing its direction. Align the tip of one arrow with the tail of the second. The vector sum is the arrow from the tail of the first to the tip of the second.

How to subtract vectors algebraically

Make one vector negative by keeping its length and changing its direction.

Length = sqrt (X²+Y²)

Direction = tan^-1(Y/X)

Resolving

Breaking a vector down into its horizontal and vertical components, which allows for 2-D motion to be analyzed with 1-D equations

How to resolve a vector into its components

Cos (𝛳) = R_X/vector length

R_X= Cos (𝛳) * vector length

Sin (𝛳) = R_Y/vector length

R_Y= Sin (𝛳) * vector length

How to build a vector from its components

Vector length = sqrt (R_X²+R_Y²)

Angle = tan^-1 (R_Y/R_X)

What are the signs of vector components for each quadrant of a graph?

I: R_X= + R_Y= +

II: R_X= - R_Y= +

III: R_X= - R_Y= -

IV: R_X= + R_Y= -

Distance

The total path taken

Distance: Symbol, unit, and scalar/vector

d, meter (m), and scalar

Displacement

Change in position

Displacement equation

Δx = x – x₀ 

Displacement: Symbol, unit, and scalar/vector

Δx (or  Δy for vertical displacement), meter (m), and vector

Position

Location relative to a chosen frame of reference

Position: Symbol, unit, and scalar/vector

Final position = x, initial position = x₀

Meters (m), vector

Average speed

Distance/time

Speed: Symbol, unit, and scalar/vector

No symbol, meters/second (m/s), scalar

Instantaneous speed

The speed at a particular moment in time

Average velocity

Change in position over change in time

Average velocity equation

Δx /Δt  (calculated using initial and final states of the object)

Average velocity: Symbol, unit, and scalar/vector

v, meters/second (m/s), and vector

Instantaneous velocity

The velocity at a particular moment in time

How to find instantaneous velocity (two ways)

1. Average velocity over a very small time interval is close to the instantaneous velocity

2. An object’s instantaneous velocity is the slope of a line tangent to a point on the graph of the object’s position as a function of time

How to find instantaneous acceleration (two ways)

1. Average acceleration over a very small time interval is close to the instantaneous acceleration

2. An object’s instantaneous acceleration is the slope of a line tangent to a point on the graph of the velocity as a function of time

Acceleration

Change in velocity over change in time

Acceleration: Symbol, units, vector/scalar

a, m/s/s or m/s², vector

Acceleration equation

Δv /Δt 

Relationship between v and a when speeding up

Same sign

Relationship between v and a when slowing down

Opposite signs

An object is accelerating if…

The magnitude and/or direction of the object’s velocity are changing

Find signs of a and v: traveling left and speeding up

v is negative, a is negative

Find signs of a and v: Traveling left and slowing down

v is negative, a is positive

Find signs of a and v: Traveling right and speeding up

v is positive, a is positive

Find signs of a and v: Traveling right and slowing down

v is positive, a is negative

Relative motion / Galilean Relativity

The motion of one thing relative to another

Reference frame

A set of coordinates that can be used to determine the position (or change in position) of objects

Inertial reference frame

A reference frame experiencing constant velocity

Choice of reference frame will determine…

The direction and magnitude of quantities observed

What property of motion of an object stays the same in all inertial reference frames?

Acceleration

From one reference frame to another, measurements can be…

Converted

Observed velocity results from…

The object’s velocity and the velocity of the reference frame (means vector addition or subtraction is needed)

Object model

When the quantities of interest are not affected by the object’s size, shape, or internal structure, the object can be represented by a single dot

What properties of an object are retained when using the object model?

Mass and charge

What properties of an object are NOT retained when using the object model?

Size, shape, internal configuration

Particle diagram / Oil Drop Diagram

Uses a dot to show the position of an object at regular intervals of time

What does it mean when a particle diagram / oil drop diagram depicts dots clumped together and then spreading apart?

The object is speeding up because later, it is covering more distance in the same amount of time

Motion Diagrams

The combination of particle diagrams with vector arrows

Slope of a position vs time graph

Velocity

Meaning of a horizontal line on a position vs time graph

Constant position (v=0 m/s)

Slope of a velocity vs time graph

Acceleration

Area under a velocity vs time graph

Change in position

Meaning of a horizontal line on a velocity vs time graph

Constant velocity

g

9.81 m/s²

Near the surface of the Earth, the vertical acceleration caused by the force of gravity is… (direction) (constant or changing) (value)

Downward, constant, and approximately 9.81m/s²

Area under an acceleration vs time graph

Change in velocity

How to interpret a curved position vs time graph

1. Decide if v is + or - (positive is bottom to top, negative is top to bottom)

2. Decide if it is speeding up or slowing down (steep to shallow = slowing down, shallow to steep = speeding up))

3. Decide on sign (slowing down = v and a are opposite signs, speeding up = v and a are the same sign)

How to interpret a curved velocity vs time graph

1. Decide is a is + or - (positive is bottom to top, negative is top to bottom)

2. Decide if a is increasing or decreasing (steep to shallow = decreasing, shallow to steep = increasing)

   1. Decide if acceleration is zero (horizontal line = acceleration is 0)

Linearization

A technique in physics to make a non-linear graph linear by plotting one quantity against another in a specific way that resembles y=mx+b

How to linearize…

y= x², y = 1/x, y = sqrt(x)

Plot y as a function of x²

Plot y as a function of 1/x

Plot y as a function of sqrt(x)

Uniformly Accelerated Motion (UAM)

Situations in which acceleration is constant

UAM equation without displacement/position

v_x= v_x0+ a_xt

UAM equation without final velocity

x = x₀ + v_x0t + ½ a_xt²

UAM equation without time

v_x²  = v_x0² + 2a_x(x - x₀)

Free fall

When an object is only acted upon by gravity

Acceleration during free fall is…

Constant and always down

g on the Moon

1.63 m/s²

Describe v and a for an object at all points in free fall

Going up: v= +, a = - (slowing down)

At the top: v = 0, a = - (no motion for an instant)

Going down: v = - a= - (speeding up)

What does the graph of velocity vs time look like for an object thrown up and coming down?

Positive velocity then negative velocity, constant negative slope means constant negative acceleration

What does the graph of velocity vs time look like for an object thrown straight down?

Starts with nonzero negative velocity, constant negative slope means constant negative acceleration

What does the graph of velocity vs time look like for an object dropped straight down?

Starts with zero velocity, constant negative slope means constant negative acceleration

If a projectile lands at the same height it started with, and there is no air resistance, the time it takes to get to the top height equals…

½ of the total time

Projectile motion

A special case of two-dimensional motion that has zero acceleration in one dimension and constant, nonzero acceleration in the second dimension

What is the only value that is the same for the horizontal and vertical directions in projectile motion?

Time

Describe v_x, v_y, a_x, and a_y for projectile motion when the object is going up

v_x = +

v_y = +

a_x = 0

a_y = -9.81

Describe v_x, v_y, a_x, and a_y for projectile motion when the object is at the top

v_x = +

v_y = 0

a_x = 0

a_y = -9.81

Describe v_x, v_y, a_x, and a_y for projectile motion when the object is going down

v_x = +

v_y = -

a_x = 0

a_y = -9.81

What does v_0x affect for a projectile?

YES: Displacement

NO: Flight time

What value affects the displacement of a projectile?

v_0x

What value affects the flight time of a projectile?

v_0y

Trajectory

The pathway that a moving object follows through space

What shape is the trajectory of a 2d projectile?

Parabola

Angle between velocity and acceleration at the top of projectile motion’s trajectory

90 degrees (perpendicular), because the only velocity is horizontal and the only acceleration is vertical

Two projectiles fired at different angles will have the same range if…

They are fired at complementary angles

Range

The horizontal displacement of a projectile

If an object is fired horizontally and another, identical object is dropped vertically…

They will hit the ground at the exact same time, but the launched object is faster

The range of a projectile is maximized when the angle is equal to…

45 degrees