Physics: Vectors, Significant Figures, and Classical Mechanics (Lecture Notes)

Vocabulary flashcards covering key terms from the notes on significant figures, scientific notation, vectors, and classical mechanics.

Significant figures

Digits that express precision in a number; nonzero digits are always significant; zeros may or may not be significant depending on position and decimal point.

Scientific notation

A way of writing numbers as C × 10^n where C is between 1 and 10, used to manage significant digits and scale.

Leading zeros

Zeros that come before the first nonzero digit; placeholders and not significant.

Captive zeros

Zeros between nonzero digits; always significant.

Trailing zeros

Zeros at the end of a number; significant if a decimal point is present; otherwise placeholders.

Vector

A quantity with both magnitude and direction, often represented by an arrow.

Scalar

A quantity with only magnitude and no direction.

Magnitude

The length or size of a vector.

Direction

The orientation of a vector, described by an angle or compass direction.

Tail (Origin)

The starting point of a vector in a diagram.

Body (Magnitude)

The main portion of a vector representing its length (magnitude).

Arrow head (Direction)

The tip of a vector indicating its direction.

Resultant

The vector obtained by adding two or more vectors.

Pythagorean theorem

In a right triangle, a^2 + b^2 = c^2; used to relate sides and compute distances.

SOH-CAH-TOA

Mnemonic for trigonometric ratios: sine = opposite/hypotenuse; cosine = adjacent/hypotenuse; tangent = opposite/adjacent.

Sine

Ratio of the opposite side to the hypotenuse in a right triangle.

Cosine

Ratio of the adjacent side to the hypotenuse in a right triangle.

Tangent

Ratio of the opposite side to the adjacent side in a right triangle.

Ax

x-component of vector A; projection along the x-axis.

Ay

y-component of vector A; projection along the y-axis.

Rx

x-component of the resultant vector R.

Ry

y-component of the resultant vector R.

Displacement

A vector representing change in position; magnitude is the straight-line distance from start to end with direction from initial to final position.

Distance

Scalar quantity representing the total ground covered, regardless of direction.

Velocity

Rate of change of position; a vector quantity with both magnitude and direction.

Speed

Rate of motion; a scalar quantity representing how fast an object is moving.

Acceleration

Rate of change of velocity; a vector quantity.

Instantaneous speed

Speed at a specific instant along the path.

Instantaneous velocity

Velocity at a specific instant or position; often represented as dx/dt.

Instantaneous acceleration

Acceleration at a specific instant.

Uniform acceleration

Motion with constant acceleration.

Free-fall

Motion under gravity only; acceleration is -9.8 m/s^2 downward; if dropped, initial velocity is 0.

Gravity

Acceleration due to Earth's gravity, approximately 9.8 m/s^2 downward.

X equation for motion

x = v_i t + 1/2 a t^2; displacement in one-dimensional motion with constant acceleration.

Velocity-squared equation

vf^2 = vi^2 + 2 a x; relates velocities, acceleration, and displacement without time.