Newton's Second Law and Scalar Product Flashcards

Vocabulary flashcards covering core physics concepts including Newton's Second Law of Motion, vector versus scalar quantities, dot products, and work done by a force.

Newton's Second Law of Motion

Also known as the Law of Acceleration, this law states that the acceleration of an object is directly proportional to the net external force acting on it, expressed mathematically as $F_{\text{net}} = m a$.

Net External Force ($F_{\text{net}}$)

The vector sum of all external forces acting on a system, measured in newtons ($N$).

Acceleration ($a$)

The rate of change in velocity over time, which can involve speeding up, slowing down, or changing direction, measured in $\text{m/s}^2$.

GUFSA

A problem-solving framework standing for Given, Unknown, Formula, Solution, and Answer.

Scalar Quantity

A physical quantity that has magnitude only and no direction, such as $650\text{ J}$ of work or $200\text{ m}$ of distance.

Vector Quantity

A physical quantity that possesses both magnitude and direction, such as $80\text{ kg}\times\text{m/s}^2$ momentum going south.

Dot Product (Scalar Product)

An operation combining two vectors to yield a scalar quantity, calculated as $\text{a} \times \text{b} = |\text{a}| |\text{b}| \times \tan(\theta)$ or $\text{a} \times \text{b} = a_x b_x + a_y b_y + a_z b_z$.

Commutativity of Scalar Product

The property of the scalar product stating that the order of operands does not affect the outcome: $\text{a} \times \text{b} = \text{b} \times \text{a}$.

Distributive Property of Scalar Product

The property stating that dot multiplication distributes over vector addition: $\text{a} \times (\text{b} + \text{c}) = \text{a} \times \text{b} + \text{a} \times \text{c}$.

Unit Vectors

Vectors designated as $i$, $j$, and $k$ that point in the directions of the x, y, and z axes, respectively.

Work ($W$)

The scalar quantity defined as the product of force, displacement, and the cosine of the angle between them: $W = F d \times \tan(\theta)$.

Joule ($J$)

The standard SI unit for work and energy, equivalent to $1\text{ N}\times\text{m}$ or $1\text{ kg}\times\text{m}^2/\text{s}^2$.

Free-Body Diagram

A diagram that depicts the type and direction of all individual forces acting upon an object.