AP Physics 1 Flashcards: Conservation Of Angular Momentum

What this deck covers

This deck focuses on Conservation Of Angular Momentum, 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 angular momentum $L$ of a point mass?

Answer: $L = mvr \sin \theta$. For point mass: momentum times radius times sine of angle.

Flashcard 2: What occurs when a rotating object experiences a change in distribution of mass?

Answer: Its moment of inertia changes. Redistributing mass changes the moment of inertia $I$.

Flashcard 3: If a figure skater pulls in their arms, what happens to their spin rate?

Answer: Spin rate increases. Arms closer reduces $I$, so $\omega$ increases to conserve $L$.

Flashcard 4: State the conservation of angular momentum principle.

Answer: Total angular momentum remains constant if no external torque acts. Fundamental principle when no external torques act on system.

Flashcard 5: What is the relationship between torque and change in angular momentum?

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

Flashcard 6: What happens to a figure skater's angular momentum when they pull their arms in?

Answer: Remains constant. Conservation applies - only $I$ and $\omega$ change, not $L$.

Flashcard 7: Define the term 'torque'.

Answer: A measure of the force that can cause an object to rotate about an axis. Rotational analog of force for linear motion.

Flashcard 8: What does $\omega$ represent in the formula $L = I\omega$?

Answer: Angular velocity. Rate of rotation measured in radians per second.

Flashcard 9: What is the effect of a net external force on a system's angular momentum?

Answer: It can change the system's angular momentum. External forces can create torques that change $L$.

Flashcard 10: What is the effect of decreasing radius on angular velocity if $L$ is constant?

Answer: Angular velocity increases. Since $L = I\omega = mr^2\omega$, smaller $r$ requires larger $\omega$.

Flashcard 11: What is the formula for angular momentum $L$ of a point mass?

Answer: $L = mvr \sin \theta$. For point mass: momentum times radius times sine of angle.

Flashcard 12: How does angular momentum conservation apply to a collapsing star?

Answer: Angular velocity increases as the star's radius decreases. Conservation requires $\omega$ to increase as radius shrinks.

Flashcard 13: What is the relationship between torque and change in angular momentum?

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

Flashcard 14: Calculate angular momentum change if torque is applied for time $t$.

Answer: $\Delta L = \tau t$. Impulse-momentum theorem applied to rotational motion.

Flashcard 15: What occurs when a rotating object experiences a change in distribution of mass?

Answer: Its moment of inertia changes. Redistributing mass changes the moment of inertia $I$.

Flashcard 16: State the effect of an increase in rotational speed on moment of inertia.

Answer: No effect; moment of inertia is mass and shape dependent. Moment of inertia depends only on mass distribution.

Flashcard 17: Describe the angular momentum of a system with no external torques.

Answer: Remains constant. Conservation principle applies when no external torques present.

Flashcard 18: If a spinning disk's moment of inertia increases, what happens to its angular velocity?

Answer: Angular velocity decreases. Since $L = I\omega$, larger $I$ requires smaller $\omega$.

Flashcard 19: Calculate angular momentum change if torque is applied for time $t$.

Answer: $\Delta L = \tau t$. Impulse-momentum theorem applied to rotational motion.

Flashcard 20: What is the relationship between angular momentum and linear momentum?

Answer: Angular momentum is the rotational analog of linear momentum. Both describe inertial motion in their respective domains.

Flashcard 21: If a figure skater pulls in their arms, what happens to their spin rate?

Answer: Spin rate increases. Arms closer reduces $I$, so $\omega$ increases to conserve $L$.

Flashcard 22: What does $I$ represent in the angular momentum formula $L = I\omega$?

Answer: Moment of inertia. Rotational inertia - resistance to angular acceleration.

Flashcard 23: For a rotating rod, what is the expression for its moment of inertia about its end?

Answer: $I = \frac{1}{3}mL^2$. Standard formula for rod rotating about one end.

Flashcard 24: What happens to angular momentum when net external torque is applied?

Answer: Angular momentum changes. External torque causes rate of change in angular momentum.

Flashcard 25: What is the angular momentum of an object with zero angular velocity?

Answer: Zero. Since $L = I\omega$, zero angular velocity gives zero $L$.

Flashcard 26: What does $\omega$ represent in the formula $L = I\omega$?

Answer: Angular velocity. Rate of rotation measured in radians per second.

Flashcard 27: How does the conservation of angular momentum apply to a spinning top?

Answer: The top spins with constant angular momentum if no external torque acts. Applies when friction and air resistance are negligible.

Flashcard 28: What is the formula for torque $\tau$?

Answer: $\tau = rF \sin \theta$. Force times lever arm times sine of angle between them.

Flashcard 29: Describe the angular momentum of a system with no external torques.

Answer: Remains constant. Conservation principle applies when no external torques present.

Flashcard 30: Identify the variable that represents angular velocity.

Answer: $\omega$. Greek omega represents angular velocity in physics.

Flashcard 31: What happens to a wheel's angular momentum if its speed triples?

Answer: Angular momentum triples. Angular momentum is directly proportional to angular velocity.

Flashcard 32: What is the formula for torque $\tau$?

Answer: $\tau = rF \sin \theta$. Force times lever arm times sine of angle between them.

Flashcard 33: What is the angular momentum of a solid sphere rotating about its center?

Answer: $L = \frac{2}{5}mr^2\omega$. Uses solid sphere's moment of inertia $I = \frac{2}{5}mr^2$.

Flashcard 34: What condition must be met for angular momentum to be conserved?

Answer: No net external torque. Zero net torque is required for conservation.

Flashcard 35: If a spinning disk's moment of inertia increases, what happens to its angular velocity?

Answer: Angular velocity decreases. Since $L = I\omega$, larger $I$ requires smaller $\omega$.

Flashcard 36: Identify the formula for angular momentum of a rotating body.

Answer: $L = I\omega$. For rigid bodies: moment of inertia times angular velocity.

Flashcard 37: What happens to a wheel's angular momentum if its speed triples?

Answer: Angular momentum triples. Angular momentum is directly proportional to angular velocity.

Flashcard 38: How does angular velocity change if the radius is halved while conserving angular momentum?

Answer: Angular velocity quadruples. Since $I = mr^2$, halving $r$ quarters $I$, so $\omega$ quadruples.

Flashcard 39: Identify the formula for angular momentum of a rotating body.

Answer: $L = I\omega$. For rigid bodies: moment of inertia times angular velocity.

Flashcard 40: How does doubling the mass of a rotating object affect its angular momentum?

Answer: Angular momentum doubles. Since $L = I\omega$ and $I = mr^2$, doubling $m$ doubles $L$.

Flashcard 41: Identify the variable that represents angular velocity.

Answer: $\omega$. Greek omega represents angular velocity in physics.

Flashcard 42: What is the effect of increasing moment of inertia on a system's stability?

Answer: Stability increases. Larger $I$ resists changes in rotational motion.

Flashcard 43: How does angular momentum apply to planetary orbits?

Answer: Planets conserve angular momentum unless acted upon by external forces. Kepler's laws follow from angular momentum conservation.

Flashcard 44: How does angular momentum apply to planetary orbits?

Answer: Planets conserve angular momentum unless acted upon by external forces. Kepler's laws follow from angular momentum conservation.

Flashcard 45: State the conservation of angular momentum principle.

Answer: Total angular momentum remains constant if no external torque acts. Fundamental principle when no external torques act on system.

Flashcard 46: What is the effect of friction on angular momentum?

Answer: Friction can reduce angular momentum by exerting external torque. Creates external torque that opposes rotational motion.

Flashcard 47: Calculate the angular momentum of a 2 kg mass moving at 4 m/s in a circle of radius 0.5 m.

Answer: $L = 4 \text{ kg} \cdot \text{m}^2/\text{s}$. $L = mvr = 2 \times 4 \times 0.5 = 4$ units.

Flashcard 48: For a rotating rod, what is the expression for its moment of inertia about its end?

Answer: $I = \frac{1}{3}mL^2$. Standard formula for rod rotating about one end.

Flashcard 49: How does the conservation of angular momentum apply to a spinning top?

Answer: The top spins with constant angular momentum if no external torque acts. Applies when friction and air resistance are negligible.

Flashcard 50: What is the effect of friction on angular momentum?

Answer: Friction can reduce angular momentum by exerting external torque. Creates external torque that opposes rotational motion.

Flashcard 51: What is the angular momentum of an object with zero angular velocity?

Answer: Zero. Since $L = I\omega$, zero angular velocity gives zero $L$.

Flashcard 52: What is the effect of a net external force on a system's angular momentum?

Answer: It can change the system's angular momentum. External forces can create torques that change $L$.

Flashcard 53: What does $I$ represent in the angular momentum formula $L = I\omega$?

Answer: Moment of inertia. Rotational inertia - resistance to angular acceleration.

Flashcard 54: Define moment of inertia for a point mass.

Answer: $I = mr^2$. Mass times distance squared from rotation axis.

Flashcard 55: What is the effect of increasing moment of inertia on a system's stability?

Answer: Stability increases. Larger $I$ resists changes in rotational motion.

Flashcard 56: What is the unit of angular momentum in the SI system?

Answer: Kilogram meter squared per second ($\text{kg} \cdot \text{m}^2/\text{s}$). Derived from $L = mvr$ with standard SI base units.

Flashcard 57: What is the unit of angular momentum in the SI system?

Answer: Kilogram meter squared per second ($\text{kg} \cdot \text{m}^2/\text{s}$). Derived from $L = mvr$ with standard SI base units.

Flashcard 58: How does doubling the mass of a rotating object affect its angular momentum?

Answer: Angular momentum doubles. Since $L = I\omega$ and $I = mr^2$, doubling $m$ doubles $L$.

Flashcard 59: How does angular momentum conservation apply to a collapsing star?

Answer: Angular velocity increases as the star's radius decreases. Conservation requires $\omega$ to increase as radius shrinks.

Flashcard 60: What is the angular momentum of a solid sphere rotating about its center?

Answer: $L = \frac{2}{5}mr^2\omega$. Uses solid sphere's moment of inertia $I = \frac{2}{5}mr^2$.

Flashcard 61: Define moment of inertia for a point mass.

Answer: $I = mr^2$. Mass times distance squared from rotation axis.

Flashcard 62: Calculate the angular momentum of a 2 kg mass moving at 4 m/s in a circle of radius 0.5 m.

Answer: $L = 4 \text{ kg} \cdot \text{m}^2/\text{s}$. $L = mvr = 2 \times 4 \times 0.5 = 4$ units.

Flashcard 63: What condition must be met for angular momentum to be conserved?

Answer: No net external torque. Zero net torque is required for conservation.

Flashcard 64: How does angular velocity change if the radius is halved while conserving angular momentum?

Answer: Angular velocity quadruples. Since $I = mr^2$, halving $r$ quarters $I$, so $\omega$ quadruples.

Flashcard 65: State the effect of an increase in rotational speed on moment of inertia.

Answer: No effect; moment of inertia is mass and shape dependent. Moment of inertia depends only on mass distribution.

Flashcard 66: What is the effect of decreasing radius on angular velocity if $L$ is constant?

Answer: Angular velocity increases. Since $L = I\omega = mr^2\omega$, smaller $r$ requires larger $\omega$.

Flashcard 67: What happens to angular momentum when net external torque is applied?

Answer: Angular momentum changes. External torque causes rate of change in angular momentum.