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: Find the angular acceleration for a $10$ kg disk with $1$ m radius and $5$ N·m torque.

Answer: $\text{α} = 1.25$ rad/s². Use $\tau = I\alpha$ where $I = \frac{1}{2}mr^2$ for disk.

Flashcard 2: 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 3: 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 4: 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 5: 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 6: 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: $I_1\omega_1 = I_2\omega_2$.

Flashcard 7: 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 8: What is the unit of angular velocity in the International System of Units (SI)?

Answer: Radians per second (rad/s). Standard SI unit for rotational motion rate.

Flashcard 9: Which quantity measures an object's resistance to changes in rotational motion?

Answer: Moment of Inertia. Inertia determines how hard it is to change rotation.

Flashcard 10: What is the unit of angular velocity in the International System of Units (SI)?

Answer: Radians per second (rad/s). Standard SI unit for rotational motion rate.

Flashcard 11: 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 12: What is the relationship between frequency ($f$) and period ($T$) of rotation?

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

Flashcard 13: 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 14: 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 15: What is the relationship between centripetal acceleration and angular velocity?

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

Flashcard 16: 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 17: What is the relationship between frequency ($f$) and period ($T$) of rotation?

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

Flashcard 18: Identify the formula relating tangential speed and angular speed.

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

Flashcard 19: What is the term for the rate of change of angular velocity?

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

Flashcard 20: 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: $I_1\omega_1 = I_2\omega_2$.

Flashcard 21: What is the linear displacement of a point $1$ m from the axis after a $2$ rad rotation?

Answer: $s = 2$ m. Arc length equals radius times angle in radians.

Flashcard 22: 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 23: 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 24: What is the rotational analog of mass in linear motion?

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

Flashcard 25: 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 26: State the formula for the period of a rotating object in terms of angular velocity.

Answer: $T = \frac{2\text{π}}{\text{ω}}$. Period is $2\pi$ divided by angular velocity.

Flashcard 27: What is the rotational analog of mass in linear motion?

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

Flashcard 28: Identify the angular displacement if a wheel turns $4$ revolutions.

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

Flashcard 29: Calculate the angular momentum of a $3$ kg·m² object rotating at $10$ rad/s.

Answer: $L = 30$ kg·m²/s. Angular momentum equals $I$ times $\omega$.

Flashcard 30: State the equation of rotational kinetic energy.

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

Flashcard 31: 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 32: What is the relationship between centripetal acceleration and angular velocity?

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

Flashcard 33: State the relationship between linear displacement ($s$) and angular displacement ($\theta$).

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

Flashcard 34: State the formula for the period of a rotating object in terms of angular velocity.

Answer: $T = \frac{2\text{π}}{\text{ω}}$. Period is $2\pi$ divided by angular velocity.

Flashcard 35: 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 36: Which principle relates torque to angular acceleration?

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

Flashcard 37: What is the formula for angular acceleration in terms of change in angular velocity and time?

Answer: $\text{Angular acceleration} = \frac{\Delta \omega}{t}$. Rate of change of angular velocity over time.

Flashcard 38: Identify the term for the rate of change of angular displacement.

Answer: Angular Velocity. The rate of change of angular position.

Flashcard 39: Identify the angular displacement if a wheel turns $4$ revolutions.

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

Flashcard 40: 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 41: What is the term for the rate of change of angular velocity?

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

Flashcard 42: 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 43: 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 44: 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 45: 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 46: 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 47: 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 48: Identify the tangential speed of a point $2$ m from the center of a wheel rotating at $3$ rad/s.

Answer: $v = 6$ m/s. Use $v = r\omega$ relationship.

Flashcard 49: Calculate the angular momentum of a $3$ kg·m² object rotating at $10$ rad/s.

Answer: $L = 30$ kg·m²/s. Angular momentum equals $I$ times $\omega$.

Flashcard 50: What is the formula for angular acceleration in terms of change in angular velocity and time?

Answer: $\text{Angular acceleration} = \frac{\text{Δω}}{t}$. Rate of change of angular velocity over time.

Flashcard 51: 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 52: 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 53: 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 54: Identify the term for the rate of change of angular displacement.

Answer: Angular Velocity. The rate of change of angular position.

Flashcard 55: State the equation of rotational kinetic energy.

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

Flashcard 56: 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 57: 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 58: 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 59: 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 60: Find the angular acceleration for a $10$ kg disk with $1$ m radius and $5$ N·m torque.

Answer: $\text{α} = 1.25$ rad/s². Use $\tau = I\alpha$ where $I = \frac{1}{2}mr^2$ for disk.

Flashcard 61: 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 62: 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 63: Determine the frequency of a rotating object with a period of $0.5$ seconds.

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