College Physics - Vectors and Trigonometry

Flashcards covering vector analysis, scalar definitions, graphical addition methods, and component resolution based on Schaum's College Physics.

In the vector diagram shown, what vector represents the sum $\vec{\mathbf{A}} + \vec{\mathbf{B}} + \vec{\mathbf{C}}$ using the polygon method?

The resultant vector $\vec{\mathbf{R}}$, drawn directly from the Start point (tail of $\vec{\mathbf{A}}$) to the End point (tip of $ rối\vec{\mathbf{C}}$$).

For the right triangle shown, what are the trigonometric definitions for $\sin(\theta)$, $\cos(\theta)$, and $\tan(\theta)$?

$\sin(\theta) = \frac{B}{C}$, $\cos(\theta) = \frac{A}{C}$, and $\tan(\theta) = \frac{B}{A}$.

What vector addition method is illustrated in the diagram showing vectors $\vec{\mathbf{A}}$ and $\vec{\mathbf{B}}$ placed tail-to-tail?

The parallelogram method, where the resultant vector $\vec{\mathbf{R}}$ is represented by the diagonal of the parallelogram formed by $\vec{\mathbf{A}}$ and $\vec{\mathbf{B}}$.

In the diagram shown, how are the rectangular components $\vec{\mathbf{R}}_x$ and $\vec{\mathbf{R}}_y$ of vector $\vec{\mathbf{R}}$ calculated?

$R_x = R \cos(\theta)$ along the $x$-axis and $R_y = R \sin(\theta)$ along the $y$-axis.

What is a scalar quantity in physics?

A physical quantity that possesses magnitude (or size) only, with no direction specified.

What is a vector quantity in physics?

A physical quantity that possesses both magnitude and direction.

What is meant by the resultant vector of a system of vectors?

A single vector that produces the same physical effect as a combination of two or more individual vectors.

How is vector subtraction $\vec{\mathbf{A}} - \vec{\mathbf{B}}$ defined in vector algebra?

It is defined as the addition of vector $\vec{\mathbf{A}}$ and the negative vector $-\vec{\mathbf{B}}$, such that $\vec{\mathbf{A}} - \vec{\mathbf{B}} = \vec{\mathbf{A}} + (-\vec{\mathbf{B}})$.

What is the negative of a vector $\vec{\mathbf{A}}$?

A vector that has the exact same magnitude as $\vec{\mathbf{A}}$, but points in the opposite direction.

How is the magnitude $R$ of a resultant vector determined from its perpendicular components $R_x$ and $R_y$?

Using the Pythagorean theorem: $R = \sqrt{R_x^2 + R_y^2}$.

How is the reference angle $\phi$ calculated when determining the direction of a resultant vector from its components?

$\tan(\phi) = \frac{|R_y|}{|R_x|}$.

What steps are involved in adding multiple vectors using the component method?

1. Resolve each vector into its $x$ and $y$ components.
2. Sum all $x$-components to find $R_x = \sum F_x$ and all $y$-components to find $R_y = \sum F_y$.
3. Calculate resultant magnitude $R = \sqrt{R_x^2 + R_y^2}$.
4. Find direction angle $\phi$ using $\tan(\phi) = \frac{|R_y|}{|R_x|}$.