Conservation of Angular Momentum - AP Physics C: Mechanics
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What does $I$ represent in the equation $L = I\omega$?
What does $I$ represent in the equation $L = I\omega$?
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Moment of inertia. The rotational inertia of the object about the axis.
Moment of inertia. The rotational inertia of the object about the axis.
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State the formula for the moment of inertia of a solid sphere.
State the formula for the moment of inertia of a solid sphere.
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$I = \frac{2}{5}mr^2$. Standard formula for uniform solid spheres rotating about center.
$I = \frac{2}{5}mr^2$. Standard formula for uniform solid spheres rotating about center.
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What happens to angular momentum if no external torque acts on a system?
What happens to angular momentum if no external torque acts on a system?
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It remains constant. Direct consequence of conservation of angular momentum.
It remains constant. Direct consequence of conservation of angular momentum.
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How does conservation of angular momentum affect a spinning ice skater's speed when she pulls in her arms?
How does conservation of angular momentum affect a spinning ice skater's speed when she pulls in her arms?
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Her speed increases. Reduced moment of inertia increases angular velocity.
Her speed increases. Reduced moment of inertia increases angular velocity.
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What is the expression for angular momentum of a rigid body with moment of inertia $I$ and angular velocity $\omega$?
What is the expression for angular momentum of a rigid body with moment of inertia $I$ and angular velocity $\omega$?
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$L = I\omega$. Standard formula for rigid body angular momentum.
$L = I\omega$. Standard formula for rigid body angular momentum.
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Calculate the angular momentum of a 3 kg mass moving at 5 m/s in a circle of radius 2 m.
Calculate the angular momentum of a 3 kg mass moving at 5 m/s in a circle of radius 2 m.
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$L = 30 \text{ kg·m}^2/\text{s}$. Using $L = mvr = 3 \times 5 \times 2 = 30$.
$L = 30 \text{ kg·m}^2/\text{s}$. Using $L = mvr = 3 \times 5 \times 2 = 30$.
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In $L = I\omega$, what does $\omega$ represent?
In $L = I\omega$, what does $\omega$ represent?
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Angular velocity. The rate of rotational motion in radians per second.
Angular velocity. The rate of rotational motion in radians per second.
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State the relationship between linear and angular momentum for a rotating object.
State the relationship between linear and angular momentum for a rotating object.
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Angular momentum is the rotational equivalent of linear momentum. Both describe momentum but for different types of motion.
Angular momentum is the rotational equivalent of linear momentum. Both describe momentum but for different types of motion.
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What is the angular momentum for a mass $m$ at distance $r$ moving with velocity $v$?
What is the angular momentum for a mass $m$ at distance $r$ moving with velocity $v$?
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$L = mvr \sin \theta$. Cross product of position and momentum vectors.
$L = mvr \sin \theta$. Cross product of position and momentum vectors.
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If a rotating system is isolated, what can be said about its angular momentum?
If a rotating system is isolated, what can be said about its angular momentum?
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It is conserved. Isolated systems have no external torques acting.
It is conserved. Isolated systems have no external torques acting.
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What is the angular momentum of a rotating disk with $I = 2 \text{ kg·m}^2$ and $\omega = 3 \text{ rad/s}$?
What is the angular momentum of a rotating disk with $I = 2 \text{ kg·m}^2$ and $\omega = 3 \text{ rad/s}$?
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6 kg·m²/s. Using $L = I\omega = 2 \times 3 = 6$.
6 kg·m²/s. Using $L = I\omega = 2 \times 3 = 6$.
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What is the angular momentum of an object with $m = 5$ kg, $r = 2$ m, and $v = 10$ m/s?
What is the angular momentum of an object with $m = 5$ kg, $r = 2$ m, and $v = 10$ m/s?
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$L = 100 \text{ kg·m}^2/\text{s}$. Using $L = mvr = 5 \times 10 \times 2 = 100$.
$L = 100 \text{ kg·m}^2/\text{s}$. Using $L = mvr = 5 \times 10 \times 2 = 100$.
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What is the relationship between angular momentum and rotational inertia?
What is the relationship between angular momentum and rotational inertia?
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$L = I\omega$. Fundamental equation linking angular momentum and rotation.
$L = I\omega$. Fundamental equation linking angular momentum and rotation.
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What is the principle of conservation of angular momentum?
What is the principle of conservation of angular momentum?
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Total angular momentum remains constant if no external torque acts. This is Newton's first law applied to rotation.
Total angular momentum remains constant if no external torque acts. This is Newton's first law applied to rotation.
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How does angular momentum relate to the rotational equivalent of linear momentum?
How does angular momentum relate to the rotational equivalent of linear momentum?
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It is the rotational equivalent. Angular momentum parallels linear momentum in rotation.
It is the rotational equivalent. Angular momentum parallels linear momentum in rotation.
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What is the effect on angular momentum if a system is isolated and no torque is applied?
What is the effect on angular momentum if a system is isolated and no torque is applied?
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Angular momentum remains constant. No external torques means angular momentum is conserved.
Angular momentum remains constant. No external torques means angular momentum is conserved.
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State the formula for the moment of inertia of a solid sphere.
State the formula for the moment of inertia of a solid sphere.
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$I = \frac{2}{5}mr^2$. Standard formula for uniform solid spheres rotating about center.
$I = \frac{2}{5}mr^2$. Standard formula for uniform solid spheres rotating about center.
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What is the effect on a rotating system's angular velocity if its radius is reduced?
What is the effect on a rotating system's angular velocity if its radius is reduced?
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The angular velocity increases. Smaller radius decreases $I$, increasing $\omega$.
The angular velocity increases. Smaller radius decreases $I$, increasing $\omega$.
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What is the angular momentum of an object with $m = 5$ kg, $r = 2$ m, and $v = 10$ m/s?
What is the angular momentum of an object with $m = 5$ kg, $r = 2$ m, and $v = 10$ m/s?
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$L = 100 \text{ kg·m}^2/\text{s}$. Using $L = mvr = 5 \times 10 \times 2 = 100$.
$L = 100 \text{ kg·m}^2/\text{s}$. Using $L = mvr = 5 \times 10 \times 2 = 100$.
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What is the relationship between angular momentum and rotational inertia?
What is the relationship between angular momentum and rotational inertia?
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$L = I\omega$. Fundamental equation linking angular momentum and rotation.
$L = I\omega$. Fundamental equation linking angular momentum and rotation.
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Name a common real-world example of conservation of angular momentum.
Name a common real-world example of conservation of angular momentum.
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A figure skater spinning. Classic demonstration of changing moment of inertia.
A figure skater spinning. Classic demonstration of changing moment of inertia.
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Explain how decreasing the radius of rotation affects angular velocity if angular momentum is conserved.
Explain how decreasing the radius of rotation affects angular velocity if angular momentum is conserved.
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Angular velocity increases. Smaller radius means larger $\omega$ to conserve $L$.
Angular velocity increases. Smaller radius means larger $\omega$ to conserve $L$.
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What does $I$ represent in the equation $L = I\omega$?
What does $I$ represent in the equation $L = I\omega$?
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Moment of inertia. The rotational inertia of the object about the axis.
Moment of inertia. The rotational inertia of the object about the axis.
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State the formula for angular momentum of a point mass.
State the formula for angular momentum of a point mass.
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$L = mvr \sin \theta$. Where $m$ is mass, $v$ is velocity, $r$ is distance, and $\theta$ is angle.
$L = mvr \sin \theta$. Where $m$ is mass, $v$ is velocity, $r$ is distance, and $\theta$ is angle.
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Which physical quantity must be conserved in a closed system with no external torques?
Which physical quantity must be conserved in a closed system with no external torques?
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Angular momentum. No external torques means no change in rotational momentum.
Angular momentum. No external torques means no change in rotational momentum.
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What happens to angular momentum if no external torque acts on a system?
What happens to angular momentum if no external torque acts on a system?
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It remains constant. Direct consequence of conservation of angular momentum.
It remains constant. Direct consequence of conservation of angular momentum.
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What is the angular momentum for a mass $m$ at distance $r$ moving with velocity $v$?
What is the angular momentum for a mass $m$ at distance $r$ moving with velocity $v$?
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$L = mvr \sin \theta$. Cross product of position and momentum vectors.
$L = mvr \sin \theta$. Cross product of position and momentum vectors.
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If a rotating system is isolated, what can be said about its angular momentum?
If a rotating system is isolated, what can be said about its angular momentum?
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It is conserved. Isolated systems have no external torques acting.
It is conserved. Isolated systems have no external torques acting.
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Calculate the angular momentum of a 2 kg mass moving in a circle of radius 3 m at 4 m/s.
Calculate the angular momentum of a 2 kg mass moving in a circle of radius 3 m at 4 m/s.
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$L = 24 \text{ kg·m}^2/\text{s}$. Using $L = mvr = 2 \times 4 \times 3 = 24$.
$L = 24 \text{ kg·m}^2/\text{s}$. Using $L = mvr = 2 \times 4 \times 3 = 24$.
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What is the unit of angular momentum in the SI system?
What is the unit of angular momentum in the SI system?
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Kilogram meter squared per second (kg·m²/s). Derived from $[M][L^2][T^{-1}]$ dimensional analysis.
Kilogram meter squared per second (kg·m²/s). Derived from $[M][L^2][T^{-1}]$ dimensional analysis.
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