AP Physics C: Mechanics Chapter 1

What is a scalar quantity?

Something that has one value but no specific direction

What is a vector quantity?

Something that has one value and a definite direction

True or false: displacement = distance

False

What is distance?

The total path traveled by an object over its course of travel

What is displacement?

The actual length and direction a particle has traveled compared to its origin/starting point

Is distance a vector or scalar quantity?

scalar

Is displacement a vector or scalar quantity?

vector

What does \overrightarrow{A} imply?

It denotes a vector

What does |\overrightarrow{A}| imply?

It denotes the magnitude of the vector

True or false: vector work with the same properties as addition and subtraction

True

How should a resultant vector be drawn?

From the start of the first vector to the endpoint of the last vector

Using addition and subtraction properties, how can \overrightarrow{A}-\overrightarrow{B} also be written?

\overrightarrow{A}+(-\overrightarrow{B})

What is the resultant vector?

The combination of two or more vectors, denoted usually as \overrightarrow{R}

What property of a vector is affected when turned negative?

the direction is reversed

What is a component?

A projection of a vector on an axis

Every vector can be broken down into how many components?

two

What are the formulas for A_x and A_y ?

A_x = Acos\theta

A_y = Asin\theta

What is the formula for A?

A = \sqrt{(A_x)²+(A_y)²}

What is the formula for \theta ?

\theta = arctan(\frac{A_y}{A_x})

What are unit vectors?

Dimensionless vectors with magnitude 1

What are the three representations of unit vectors?

\hat{i}, \hat{j}, \hat{k}

In a right-handed coordinate plane, all unit vectors are _________ to each other

perpendicular

Using unit vectors, what can A_x , A_y , and A_z be written as?

A_x = A_x\hat{i}

A_y = A_x\hat{j}

A_z = A_z\hat{k}

Using unit vectors, what can \overrightarrow{A} be represented as?

\overrightarrow{A} = A_x\hat{i} + A_y\hat{j}

Without using unit vectors, what can R_x and R_y be written as?

R_x = A_x + B_x

R_y = A_y + B_y

True or false: x\hat{i} and y\hat{j} are not valid representations of x and y

False, both are valid representations of each other

Using unit vectors, what can \vec{R} be written as?

For 2D planes:

(A_x + B_x)\hat{i} + (A_y + B_y)\hat{j}

or

A_x\hat{i} + B_x\hat{i} + A_y\hat{j} + B_y\hat{j}

or

R\hat{i} + R\hat{j}

For 3D planes:

(A_x + B_x)\hat{i} + (A_y + B_y)\hat{j} + (A_z + B_z)\hat{k}

or

A_x\hat{i} + B_x\hat{i} + A_y\hat{j} + B_y\hat{j} + A_z\hat{k} + B_z\hat{k}

or

R\hat{i} +R\hat{j} + R\hat{k}

All formulas assume the addition of 2 vectors, any additional vectors can be input into the formula (i.e., +C_x or + D_z, etc)

What is the formula for R?

R = \sqrt{(R_x)²+(R_y)²+(R_z)²}

What is the formula for \theta_x ?

\theta_x = arccos(\frac{R_x}{R})

What is the formula for V_xavg ?

V_xavg = \frac{x_f - x_i}{t_f - t_i}

What is the formula for average acceleration?

a = \frac{v_f - v_i}{t_f - t_i}

What is the formula for x_f?

x_f = x_i + v_x\Delta{t}

In AP Physics, does acceleration mean average or instantaneous acceleration?

Instantaneous

When does t_{up} = t_{down} ?

When the motion of an object is symmetrical

When does v = -v_0 ?

When the motion of an object is symmetrical

When can the motion of an object be broken down into various parts?

When the motion of an object is not symmetrical

What is the first kinematics equation?

v_x = v_{x0} + a_xt

What is the second kinematics equation?

x = x_0 +v_{x0}t + \frac{1}{2}a_xt

What is the third kinematics equation?

v_x² = v_{x0}²+2a_x(x-x_0)

True or false: two observers relative to each other will always agree on the outcome of an experiment

false

What is the equation positions seem from 2 reference framed connected to velocity?

\overrightarrow{r}_{PA} = \overrightarrow{r}_{PB} + \overrightarrow{v}_{BA}t

What is the derivative for the position equation (2 reference frames)

\overrightarrow{U}_{PA} = \overrightarrow{U}_{PB} + \overrightarrow{v}_{BA}

What is the formula for tangential velocity?

v_{tan}=r\omega

What is the formula for centripetal acceleration?

a_c=\frac{v²}{r}

What is the formula for the range of a projectile?

R=\frac{v_i²sin(2\theta)}{g}

What is the formula for the height of a launched projectile?

h=\frac{v_i²sin²(\theta)}{2g}

What is the formula for the time interval of a launched projectile?

t=\frac{2v_{yi}}{a_y}
Note, assumes the time for an object to reach its original launch height

What is the formula for the horizontal displacement of a launched projectile?

d_x=v_icos(\theta)\Delta{t}