AP Physics 1 Flashcards: Vectors And Motion In Two Dimensions

What this deck covers

This deck focuses on Vectors And Motion In Two Dimensions, giving you a quick way to review the definitions, rules, and examples that matter most for AP Physics 1.

How to use these flashcards

Work through these flashcards in short sessions. Try to answer each prompt before flipping the card, then revisit any cards you miss until the explanation feels automatic.

Flashcard 1: State the formula for angular displacement.

Answer: $\theta = \omega t$. Angle equals rate times time.

Flashcard 2: State the formula for the magnitude of a vector $(x, y)$.

Answer: $\text{Magnitude} = \sqrt{x^2 + y^2}$. Pythagorean theorem for vector length.

Flashcard 3: What is the horizontal component of velocity for a projectile at launch speed $v$ and angle $\theta$?

Answer: $v \cos \theta$. Horizontal component stays constant.

Flashcard 4: What is the formula for the cross product magnitude of $(a_1, b_1)$ and $(a_2, b_2)$?

Answer: $|a_1 b_2 - a_2 b_1|$. 2D cross product magnitude formula.

Flashcard 5: What is the resultant vector of $(3, 4)$ and $(1, 2)$?

Answer: $(4, 6)$. Add corresponding components.

Flashcard 6: Identify the unit vector in the direction of $(6, 8)$.

Answer: $(0.6, 0.8)$. Divide by magnitude $\sqrt{6^2 + 8^2} = 10$.

Flashcard 7: What is the effect of air resistance on projectile motion?

Answer: It decreases range and height. Air drag opposes motion.

Flashcard 8: What is the definition of a vector quantity?

Answer: A quantity with both magnitude and direction. Combines size and direction info.

Flashcard 9: State the formula for the maximum height of a projectile.

Answer: $h = \frac{v^2 \sin^2 \theta}{2g}$. From energy or kinematics.

Flashcard 10: What is the direction of centripetal force in circular motion?

Answer: Toward the center of the circle. Keeps object in circular path.

Flashcard 11: State the formula for centripetal acceleration.

Answer: $a_c = \frac{v^2}{r}$. Acceleration toward center.

Flashcard 12: What is the relationship between period and frequency?

Answer: $T = \frac{1}{f}$. Period and frequency are reciprocals.

Flashcard 13: What variable represents angular velocity?

Answer: $\omega$. Greek omega represents rotation rate.

Flashcard 14: Identify the unit of angular acceleration.

Answer: $\text{rad/s}^2$. Angular acceleration measured in radians.

Flashcard 15: What is the range formula for a projectile launched at $v$ and angle $\theta$?

Answer: $R = \frac{v^2 \sin 2\theta}{g}$. Uses $\sin(2\theta)$ identity.

Flashcard 16: Which factor remains constant in a projectile's horizontal motion?

Answer: Horizontal velocity. No horizontal acceleration exists.

Flashcard 17: What is the angle between vectors $(1, 0)$ and $(0, 1)$?

Answer: $90^{\circ}$. Unit vectors along axes are perpendicular.

Flashcard 18: What is the two-dimensional motion with constant acceleration called?

Answer: Projectile motion. Motion under gravity in two dimensions.

Flashcard 19: Define the term 'scalar quantity'.

Answer: A quantity with magnitude only. No directional information included.

Flashcard 20: Define the term 'scalar quantity'.

Answer: A quantity with magnitude only. No directional information included.

Flashcard 21: What is the cross product of vectors used to find?

Answer: Vector perpendicular to both vectors. Cross product creates perpendicular vector.

Flashcard 22: What is the formula for the gravitational potential energy of an object?

Answer: $U = mgh$. Height-dependent gravitational energy.

Flashcard 23: Which operation combines two vectors to form a resultant vector?

Answer: Vector addition. Forms resultant from two vectors.

Flashcard 24: Which factor remains constant in a projectile's horizontal motion?

Answer: Horizontal velocity. No horizontal acceleration exists.

Flashcard 25: Identify the velocity of a projectile at its highest point.

Answer: Zero vertical velocity. Instantaneously stops rising.

Flashcard 26: What is the scalar product used for in vector calculations?

Answer: Calculating work done. Dot product gives work value.

Flashcard 27: What is the two-dimensional motion with constant acceleration called?

Answer: Projectile motion. Motion under gravity in two dimensions.

Flashcard 28: State the component form of vector $\textbf{A}$ with magnitude $5$ at $30^{\circ}$.

Answer: $(4.33, 2.5)$. Use $x = 5\cos(30°)$, $y = 5\sin(30°)$.

Flashcard 29: State the formula for the dot product of vectors $(a_1, b_1)$ and $(a_2, b_2)$.

Answer: $a_1 a_2 + b_1 b_2$. Multiply corresponding components and sum.

Flashcard 30: What is the formula for the gravitational potential energy of an object?

Answer: $U = mgh$. Height-dependent gravitational energy.

Flashcard 31: State the formula for the dot product of vectors $(a_1, b_1)$ and $(a_2, b_2)$.

Answer: $a_1 a_2 + b_1 b_2$. Multiply corresponding components and sum.

Flashcard 32: Identify the unit vector in the direction of $(6, 8)$.

Answer: $(0.6, 0.8)$. Divide by magnitude $\sqrt{6^2 + 8^2} = 10$.

Flashcard 33: What is the cross product of vectors used to find?

Answer: Vector perpendicular to both vectors. Cross product creates perpendicular vector.

Flashcard 34: What is the dot product of vectors $(2, 3)$ and $(4, -1)$?

Answer: $5$. $(2)(4) + (3)(-1) = 8 - 3 = 5$.

Flashcard 35: Identify the velocity of a projectile at its highest point.

Answer: Zero vertical velocity. Instantaneously stops rising.

Flashcard 36: Identify the vertical component of velocity for a projectile at launch speed $v$ and angle $\theta$.

Answer: $v \sin \theta$. Initial vertical velocity component.

Flashcard 37: State the formula for the maximum height of a projectile.

Answer: $h = \frac{v^2 \sin^2 \theta}{2g}$. From energy or kinematics.

Flashcard 38: Identify the unit of angular acceleration.

Answer: $\text{rad/s}^2$. Angular acceleration measured in radians.

Flashcard 39: What is the angle between vectors $(1, 0)$ and $(0, 1)$?

Answer: $90^{\circ}$. Unit vectors along axes are perpendicular.

Flashcard 40: What is the projection of vector $\textbf{A}$ onto vector $\textbf{B}$?

Answer: $\frac{\textbf{A} \cdot \textbf{B}}{||\textbf{B}||}$. Component of A along B direction.

Flashcard 41: What is the formula for the velocity of an object in circular motion?

Answer: $v = r \omega$. Links linear and angular motion.

Flashcard 42: What is the direction of centripetal force in circular motion?

Answer: Toward the center of the circle. Keeps object in circular path.

Flashcard 43: What is the relationship between period and frequency?

Answer: $T = \frac{1}{f}$. Period and frequency are reciprocals.

Flashcard 44: What is the projection of vector $\textbf{A}$ onto vector $\textbf{B}$?

Answer: $\frac{\textbf{A} \cdot \textbf{B}}{||\textbf{B}||}$. Component of A along B direction.

Flashcard 45: What is the resultant vector of $(3, 4)$ and $(1, 2)$?

Answer: $(4, 6)$. Add corresponding components.

Flashcard 46: State the relationship between linear speed and angular speed.

Answer: $v = r \omega$. Fundamental circular motion relationship.

Flashcard 47: What is the formula for the velocity of an object in circular motion?

Answer: $v = r \omega$. Links linear and angular motion.

Flashcard 48: Identify the vertical component of velocity for a projectile at launch speed $v$ and angle $\theta$.

Answer: $v \sin \theta$. Initial vertical velocity component.

Flashcard 49: Find the vector sum of $(1, 2, 3)$ and $(4, 5, 6)$.

Answer: $(5, 7, 9)$. Add components: $(1+4, 2+5, 3+6)$.

Flashcard 50: State the component form of vector $\textbf{A}$ with magnitude $5$ at $30^{\circ}$.

Answer: $(4.33, 2.5)$. Use $x = 5\cos(30°)$, $y = 5\sin(30°)$.

Flashcard 51: What does the magnitude of the cross product represent?

Answer: Area of the parallelogram formed. Geometric interpretation of cross product.

Flashcard 52: What is the formula for the cross product magnitude of $(a_1, b_1)$ and $(a_2, b_2)$?

Answer: $|a_1 b_2 - a_2 b_1|$. 2D cross product magnitude formula.

Flashcard 53: What is the range formula for a projectile launched at $v$ and angle $\theta$?

Answer: $R = \frac{v^2 \sin 2\theta}{g}$. Uses $\sin(2\theta)$ identity.

Flashcard 54: State the relationship between linear speed and angular speed.

Answer: $v = r \omega$. Fundamental circular motion relationship.

Flashcard 55: What is the formula for work done by a force in the direction of displacement?

Answer: $W = Fd \cos \theta$. Force component in displacement direction.

Flashcard 56: What is the formula for work done by a force in the direction of displacement?

Answer: $W = Fd \cos \theta$. Force component in displacement direction.

Flashcard 57: What is the acceleration due to gravity in projectile motion?

Answer: $9.8 \text{ m/s}^2$ downward. Standard gravity near Earth's surface.

Flashcard 58: Which operation combines two vectors to form a resultant vector?

Answer: Vector addition. Forms resultant from two vectors.

Flashcard 59: What is the scalar product used for in vector calculations?

Answer: Calculating work done. Dot product gives work value.

Flashcard 60: What is the effect of air resistance on projectile motion?

Answer: It decreases range and height. Air drag opposes motion.

Flashcard 61: Find the vector sum of $(1, 2, 3)$ and $(4, 5, 6)$.

Answer: $(5, 7, 9)$. Add components: $(1+4, 2+5, 3+6)$.

Flashcard 62: What does the magnitude of the cross product represent?

Answer: Area of the parallelogram formed. Geometric interpretation of cross product.

Flashcard 63: State the formula for the magnitude of a vector $(x, y)$.

Answer: $\text{Magnitude} = \sqrt{x^2 + y^2}$. Pythagorean theorem for vector length.

Flashcard 64: What is the definition of a vector quantity?

Answer: A quantity with both magnitude and direction. Combines size and direction info.

Flashcard 65: What is the acceleration due to gravity in projectile motion?

Answer: $9.8 \text{ m/s}^2$ downward. Standard gravity near Earth's surface.

Flashcard 66: What is the dot product of vectors $(2, 3)$ and $(4, -1)$?

Answer: $5$. $(2)(4) + (3)(-1) = 8 - 3 = 5$.

Flashcard 67: What condition indicates two vectors are perpendicular?

Answer: Dot product equals zero. Orthogonal vectors have zero dot product.

Flashcard 68: State the formula for angular displacement.

Answer: $\theta = \omega t$. Angle equals rate times time.

Flashcard 69: What variable represents angular velocity?

Answer: $\omega$. Greek omega represents rotation rate.

Flashcard 70: What is the horizontal component of velocity for a projectile at launch speed $v$ and angle $\theta$?

Answer: $v \cos \theta$. Horizontal component stays constant.

Flashcard 71: What condition indicates two vectors are perpendicular?

Answer: Dot product equals zero. Orthogonal vectors have zero dot product.