AP Physics 1 Flashcards: Rotational Kinematics

What this deck covers

This deck focuses on Rotational Kinematics, 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 moment of inertia of a $2$ kg mass at $3$ m from the axis.

Answer: $I = 18$ kg·m². Use $I = mr^2$ with given mass and distance.

Flashcard 2: What is the term for the rate of change of angular velocity?

Answer: Angular Acceleration. The rate of change of angular velocity.

Flashcard 3: Calculate the period of rotation for an object rotating at $5$ rad/s.

Answer: $T = \frac{2\text{π}}{5}$ s. Period equals $2\pi$ divided by angular velocity.

Flashcard 4: State the relationship between linear velocity ($v$) and angular velocity ($\text{ω}$).

Answer: $v = r\text{ω}$. Linear velocity equals radius times angular velocity.

Flashcard 5: State the equation of rotational kinetic energy.

Answer: $K = \frac{1}{2}I\text{ω}^2$. Rotational analog of linear kinetic energy.

Flashcard 6: What is the formula for rotational work done by a torque through an angle?

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

Flashcard 7: What is the relationship between frequency ($f$) and period ($T$) of rotation?

Answer: $f = \frac{1}{T}$. Frequency is the reciprocal of period.

Flashcard 8: What is the rotational analog of mass in linear motion?

Answer: Moment of Inertia. Rotational inertia measures resistance to angular acceleration.

Flashcard 9: State the relationship between torque and angular momentum change.

Answer: $\tau = \frac{dL}{dt}$. Torque equals the time rate of change of angular momentum.

Flashcard 10: Determine the torque if a $5$ N force is applied $0.5$ m from the pivot.

Answer: $\tau = 2.5$ N·m. Torque equals force times perpendicular distance.

Flashcard 11: What is the formula for the torque ($\tau$) acting on a rotating object?

Answer: $\tau = rF\text{sin}(\theta)$. Torque depends on force, distance, and angle.

Flashcard 12: Determine the frequency of a rotating object with a period of $0.5$ seconds.

Answer: $f = 2$ Hz. Frequency equals one divided by period.

Flashcard 13: Identify the formula relating tangential speed and angular speed.

Answer: $v_{\text{tangential}} = r\text{ω}$. Tangential speed at distance $r$ from rotation axis.

Flashcard 14: Identify the formula for moment of inertia for a point mass.

Answer: $I = mr^2$. Moment of inertia for a point mass at distance $r$.

Flashcard 15: Calculate the moment of inertia of a $2$ kg mass at $3$ m from the axis.

Answer: $I = 18$ kg·m². Use $I = mr^2$ with given mass and distance.

Flashcard 16: Identify the formula for centripetal acceleration in terms of velocity and radius.

Answer: $a_c = \frac{v^2}{r}$. Acceleration directed toward the center of circular motion.

Flashcard 17: State the relationship between linear displacement ($s$) and angular displacement ($\theta$).

Answer: $s = r\theta$. Arc length equals radius times angular displacement.

Flashcard 18: Find the angular velocity if a wheel rotates $180$ degrees in $2$ seconds.

Answer: $\text{ω} = 1.57$ rad/s. Convert $180°$ to $\pi$ rad, then divide by time.

Flashcard 19: Identify the formula for angular velocity in terms of angular displacement and time.

Answer: $\text{Angular velocity} = \frac{\theta}{t}$. Angular velocity equals angular displacement divided by time.

Flashcard 20: Which principle relates torque to angular acceleration?

Answer: Newton's Second Law for Rotation. States that net torque equals $I\alpha$.

Flashcard 21: What is the relationship between centripetal acceleration and angular velocity?

Answer: $a_c = r \omega^2$. Alternative form using angular velocity and radius.

Flashcard 22: State the formula for the centripetal force required for circular motion.

Answer: $F_c = \frac{mv^2}{r}$. Force needed to maintain circular motion.

Flashcard 23: State the formula for angular displacement in terms of initial and final angle.

Answer: $\theta = \theta_f - \theta_i$. Angular displacement is the change in angular position.

Flashcard 24: Determine rotational kinetic energy of a $2$ kg·m² disk rotating at $4$ rad/s.

Answer: $K = 16$ J. Use $K = \frac{1}{2}I\omega^2$ formula.

Flashcard 25: Find the centripetal acceleration of a point on a wheel $0.2$ m from the center, rotating at $10$ rad/s.

Answer: $a_c = 20$ m/s². Use $a_c = r\omega^2$ formula.

Flashcard 26: State the unit of angular acceleration in the International System of Units (SI).

Answer: Radians per second squared (rad/s²). Standard SI unit for rotational acceleration.

Flashcard 27: Identify the angular displacement if a wheel turns $4$ revolutions.

Answer: $\theta = 8\text{π}$ rad. One revolution equals $2\pi$ radians.

Flashcard 28: Identify the conservation law applicable to a closed system with no external torques.

Answer: Conservation of Angular Momentum. Angular momentum remains constant without external torques.

Flashcard 29: What is the formula for angular momentum ($L$) of a rotating object?

Answer: $L = I\text{ω}$. Angular momentum equals moment of inertia times angular velocity.

Flashcard 30: What is the new angular velocity if a $2$ kg·m² object increases its moment of inertia to $4$ kg·m²?

Answer: $\text{ω}_{\text{new}} = \frac{1}{2}\text{ω}_{\text{initial}}$. Conservation of angular momentum: $I_1\omega_1 = I_2\omega_2$.