AP Physics 1 Flashcards: Connecting Linear And Rotational Motion

What this deck covers

This deck focuses on Connecting Linear And Rotational Motion, 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: Calculate the torque for a force of $10 \text{ N}$ applied at $2 \text{ m}$ from the pivot.

Answer: $\tau = 20 \text{ Nm}$. Apply $\tau = rF$: $\tau = 2 \times 10 = 20$ Nm.

Flashcard 2: What is the formula for the total acceleration of a point on a rotating body?

Answer: $a_{total} = \text{√}(a_t^2 + a_c^2)$. Pythagorean sum of tangential and centripetal accelerations.

Flashcard 3: Calculate the angular momentum for a point mass with mass $m = 2 \text{ kg}$, radius $r = 3 \text{ m}$, and velocity $v = 4 \text{ m/s}$.

Answer: $L = 24 \text{ kg m}^2/\text{s}$. Apply $L = mvr$: $L = 2 \times 4 \times 3 = 24$ kg⋅m²/s.

Flashcard 4: Find the linear velocity for an object rotating at $\theta = 4 \text{ rad/s}$ with radius $r = 0.5 \text{ m}$.

Answer: $v = 2 \text{ m/s}$. Apply $v = r\omega$: $v = 0.5 \times 4 = 2$ m/s.

Flashcard 5: What is the formula for the centripetal acceleration in terms of linear velocity and radius?

Answer: $a_c = \frac{v^2}{r}$. Standard formula for centripetal acceleration.

Flashcard 6: Identify the unit of torque.

Answer: Newton meter (Nm). SI unit for torque measurement.

Flashcard 7: State the formula for torque in terms of force and radius.

Answer: $\tau = r \times F$. Torque equals force times perpendicular distance from pivot.

Flashcard 8: State the equation for the work done by torque over an angular displacement.

Answer: $W = \tau \times \theta$. Rotational work equals torque times angular displacement.

Flashcard 9: What is the moment of inertia for a solid cylinder about its central axis?

Answer: $I = \frac{1}{2} m \times r^2$. Standard formula for solid cylinder rotating about its axis.

Flashcard 10: What is the formula for angular momentum in terms of mass, velocity, and radius?

Answer: $L = mvr$. Angular momentum for linear motion in circular path.

Flashcard 11: What is the unit of angular velocity?

Answer: Radians per second (rad/s). Standard SI unit for angular velocity measurement.

Flashcard 12: Calculate the tangential acceleration for $\beta = 5 \text{ rad/s}^2$ and $r = 0.3 \text{ m}$.

Answer: $a_t = 1.5 \text{ m/s}^2$. Apply $a_t = r\alpha$: $a_t = 0.3 \times 5 = 1.5 \text{ m/s}^2$.

Flashcard 13: Calculate the centripetal acceleration for $v = 5 \text{ m/s}$ and $r = 2 \text{ m}$.

Answer: $a_c = 12.5 \text{ m/s}^2$. Apply $a_c = v^2/r$: $a_c = 5^2/2 = 12.5 \text{ m/s}^2$.

Flashcard 14: Calculate the centripetal acceleration for $v = 5 \text{ m/s}$ and $r = 2 \text{ m}$.

Answer: $a_c = 12.5 \text{ m/s}^2$. Apply $a_c = v^2/r$: $a_c = 5^2/2 = 12.5 \text{ m/s}^2$.

Flashcard 15: What is the relationship between linear displacement and angular displacement?

Answer: $s = r \times \theta$. Arc length equals radius times angle in radians.

Flashcard 16: Calculate the moment of inertia for a hoop with mass $m = 5 \text{ kg}$ and radius $r = 1 \text{ m}$.

Answer: $I = 5 \text{ kg m}^2$. For a hoop, $I = mr^2$: $I = 5 \times 1^2 = 5$ kg⋅m².

Flashcard 17: What is the linear distance traveled by a point on the rim of a wheel with radius $r$ after one revolution?

Answer: $d = 2\text{π}r$. Circumference of circle with radius $r$.

Flashcard 18: Convert an angular velocity of $3 \text{ rad/s}$ to linear velocity if $r = 2 \text{ m}$.

Answer: $v = 6 \text{ m/s}$. Apply $v = r\omega$: $v = 2 \times 3 = 6$ m/s.

Flashcard 19: Find the angular acceleration if the tangential acceleration is $8 \text{ m/s}^2$ and the radius is $4 \text{ m}$.

Answer: $\beta = 2 \text{ rad/s}^2$. Apply $\alpha = a_t/r$: $\alpha = 8/4 = 2 \text{ rad/s}^2$.

Flashcard 20: Calculate the angular velocity for a wheel with $v = 10 \text{ m/s}$ and $r = 2 \text{ m}$.

Answer: $\theta = 5 \text{ rad/s}$. Apply $\omega = v/r$: $\omega = 10/2 = 5 \text{ rad/s}$

Flashcard 21: Calculate the rotational kinetic energy of a disc with $I = 2 \text{ kg m}^2$ and $\theta = 3 \text{ rad/s}$.

Answer: $KE_{rot} = 9 \text{ J}$. Apply $KE = \frac{1}{2}I\omega^2$: $KE = \frac{1}{2} \times 2 \times 3^2 = 9$ J.

Flashcard 22: What is the relationship between work done and torque in rotational motion?

Answer: $W = \tau \times \theta$. Work done equals torque times angular displacement.

Flashcard 23: What is the formula for the centripetal acceleration in terms of linear velocity and radius?

Answer: $a_c = \frac{v^2}{r}$. Standard formula for centripetal acceleration.

Flashcard 24: What is the moment of inertia for a solid cylinder about its central axis?

Answer: $I = \frac{1}{2} m \times r^2$. Standard formula for solid cylinder rotating about its axis.

Flashcard 25: What is the equation for the moment of inertia of a point mass?

Answer: $I = m \times r^2$. For a point mass at distance $r$ from the axis.

Flashcard 26: Identify the unit for moment of inertia.

Answer: Kilogram meter squared (kg m$^2$). SI unit for moment of inertia.

Flashcard 27: Find the angular momentum for $I = 8 \text{ kg m}^2$ and $\theta = 3 \text{ rad/s}$.

Answer: $L = 24 \text{ kg m}^2/\text{s}$. Apply $L = I\omega$: $L = 8 \times 3 = 24$ kg⋅m²/s.

Flashcard 28: Convert an angular velocity of $3 \text{ rad/s}$ to linear velocity if $r = 2 \text{ m}$.

Answer: $v = 6 \text{ m/s}$. Apply $v = r\omega$: $v = 2 \times 3 = 6$ m/s.

Flashcard 29: Convert a linear velocity of $5 \text{ m/s}$ to angular velocity for $r = 0.5 \text{ m}$.

Answer: $\theta = 10 \text{ rad/s}$. Apply $\omega = v/r$: $\omega = 5/0.5 = 10$ rad/s.