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