AP Physics 1 Flashcards: Rolling

What this deck covers

This deck focuses on Rolling, 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: What is the formula for the work done by torque on a rolling object?

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

Flashcard 2: What is the equation for the translational kinetic energy of a rolling object?

Answer: $KE_{\text{trans}} = \frac{1}{2} mv^2$. Translational KE depends on mass and linear velocity squared.

Flashcard 3: What is the moment of inertia of a hollow cylinder rolling about its central axis?

Answer: $I = m r^2$. For a thin-walled cylinder, all mass is at radius $r$.

Flashcard 4: What is the condition for rolling without slipping?

Answer: $v = r \theta$. For no slipping, contact point velocity equals zero.

Flashcard 5: What is the expression for the angular displacement of a rolling object?

Answer: $\theta = \frac{s}{r}$. Angular displacement equals arc length divided by radius.

Flashcard 6: Find the rolling distance given angular displacement $\theta$ and radius $r$.

Answer: $s = r \theta$. Rolling distance equals radius times angular displacement.

Flashcard 7: What is the formula for the moment of inertia of a solid cylinder rolling about its central axis?

Answer: $I = \frac{1}{2} m r^2$. For a solid cylinder, moment of inertia equals half mass times radius squared.

Flashcard 8: State the formula for the total mechanical energy of a rolling object.

Answer: $E = KE_{\text{trans}} + KE_{\text{rot}}$. Total energy is the sum of translational and rotational kinetic energies.

Flashcard 9: What is the formula for the centripetal force on a rolling object?

Answer: $F_c = \frac{mv^2}{r}$. Centripetal force equals mass times velocity squared over radius.

Flashcard 10: What is the moment of inertia for a thin spherical shell rolling about its central axis?

Answer: $I = \frac{2}{3} m r^2$. For a hollow sphere, $I$ is two-thirds of $mr^2$.

Flashcard 11: What is the formula for potential energy of a rolling object at height $h$?

Answer: $PE = mgh$. Gravitational potential energy depends on mass, gravity, and height.

Flashcard 12: What is the moment of inertia for a solid sphere rolling about its central axis?

Answer: $I = \frac{2}{5} m r^2$. For a solid sphere, $I$ is two-fifths of $mr^2$.

Flashcard 13: Calculate the moment of inertia for a ring rolling about its central axis.

Answer: $I = m r^2$. For a thin ring, all mass is concentrated at radius $r$.

Flashcard 14: What is the condition for rolling without slipping?

Answer: $v = r \theta$. For no slipping, contact point velocity equals zero.

Flashcard 15: What is the moment of inertia for a solid sphere rolling about its central axis?

Answer: $I = \frac{2}{5} m r^2$. For a solid sphere, $I$ is two-fifths of $mr^2$.

Flashcard 16: State the formula for the total mechanical energy of a rolling object.

Answer: $E = KE_{\text{trans}} + KE_{\text{rot}}$. Total energy is the sum of translational and rotational kinetic energies.

Flashcard 17: What is the moment of inertia of a hollow cylinder rolling about its central axis?

Answer: $I = m r^2$. For a thin-walled cylinder, all mass is at radius $r$.

Flashcard 18: What is the formula for the work done by torque on a rolling object?

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

Flashcard 19: Calculate the moment of inertia for a ring rolling about its central axis.

Answer: $I = m r^2$. For a thin ring, all mass is concentrated at radius $r$.

Flashcard 20: Find the rolling distance given angular displacement $\theta$ and radius $r$.

Answer: $s = r \theta$. Rolling distance equals radius times angular displacement.

Flashcard 21: What is the expression for the angular displacement of a rolling object?

Answer: $\theta = \frac{s}{r}$. Angular displacement equals arc length divided by radius.

Flashcard 22: What is the formula for potential energy of a rolling object at height $h$?

Answer: $PE = mgh$. Gravitational potential energy depends on mass, gravity, and height.

Flashcard 23: What is the moment of inertia for a thin spherical shell rolling about its central axis?

Answer: $I = \frac{2}{3} m r^2$. For a hollow sphere, $I$ is two-thirds of $mr^2$.

Flashcard 24: What is the equation for the translational kinetic energy of a rolling object?

Answer: $KE_{\text{trans}} = \frac{1}{2} mv^2$. Translational KE depends on mass and linear velocity squared.

Flashcard 25: What is the formula for the centripetal force on a rolling object?

Answer: $F_c = \frac{mv^2}{r}$. Centripetal force equals mass times velocity squared over radius.

Flashcard 26: What is the formula for the moment of inertia of a solid cylinder rolling about its central axis?

Answer: $I = \frac{1}{2} m r^2$. For a solid cylinder, moment of inertia equals half mass times radius squared.

Flashcard 27: What is the rolling-without-slipping condition relating $v_{cm}$ and $\omega$ for radius $R$?

Answer: $v_{cm}=\omega R$. Center of mass velocity equals angular velocity times radius for pure rolling.

Flashcard 28: What is the parallel-axis theorem for moment of inertia?

Answer: $I=I_{cm}+md^2$. Relates moment of inertia about any axis to that about center of mass.

Flashcard 29: What is the speed of a point on the rim at the top of a rolling wheel (relative to ground)?

Answer: $v_{top}=2v_{cm}$. Top point moves at $v_{cm}$ plus rim speed $\omega R = v_{cm}$.

Flashcard 30: What is the instantaneous speed of the contact point on a rolling wheel (relative to ground)?

Answer: $v_{contact}=0$. Contact point is instantaneous center of rotation for pure rolling.