Angular Momentum and Angular Impulse - AP Physics 1
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What is the symbol for angular momentum?
What is the symbol for angular momentum?
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$L$. Standard symbol for angular momentum in physics.
$L$. Standard symbol for angular momentum in physics.
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What is the moment of inertia for a point mass?
What is the moment of inertia for a point mass?
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$I = mr^2$. All mass concentrated at distance $r$ from axis.
$I = mr^2$. All mass concentrated at distance $r$ from axis.
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What is the formula for torque in terms of force and lever arm?
What is the formula for torque in terms of force and lever arm?
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$\tau = rF\sin(\theta)$. Force times perpendicular distance from axis.
$\tau = rF\sin(\theta)$. Force times perpendicular distance from axis.
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Which equation represents the relationship between torque and angular acceleration?
Which equation represents the relationship between torque and angular acceleration?
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$\tau = I\alpha$. Newton's second law for rotational motion.
$\tau = I\alpha$. Newton's second law for rotational motion.
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What is the angular momentum of a solid sphere rotating at angular velocity $\omega$?
What is the angular momentum of a solid sphere rotating at angular velocity $\omega$?
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$L = I \omega = \frac{2}{5}mr^2 \omega$. Uses the solid sphere moment of inertia formula.
$L = I \omega = \frac{2}{5}mr^2 \omega$. Uses the solid sphere moment of inertia formula.
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Which equation represents the relationship between torque and angular acceleration?
Which equation represents the relationship between torque and angular acceleration?
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$\tau = I\alpha$. Newton's second law for rotational motion.
$\tau = I\alpha$. Newton's second law for rotational motion.
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What is the effect of increasing $r$ on $L$ if $v$ is constant?
What is the effect of increasing $r$ on $L$ if $v$ is constant?
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$L$ increases. Angular momentum proportional to radius for fixed velocity.
$L$ increases. Angular momentum proportional to radius for fixed velocity.
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What is the angular momentum of a rotating rod about its center?
What is the angular momentum of a rotating rod about its center?
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$L = \frac{1}{12}mL^2 \omega$. Uses rod's moment of inertia about center.
$L = \frac{1}{12}mL^2 \omega$. Uses rod's moment of inertia about center.
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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 moment of inertia for solid sphere.
$I = \frac{2}{5}mr^2$. Standard moment of inertia for solid sphere.
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What is the moment of inertia for a point mass?
What is the moment of inertia for a point mass?
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$I = mr^2$. All mass concentrated at distance $r$ from axis.
$I = mr^2$. All mass concentrated at distance $r$ from axis.
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What is the angular momentum of a disk rotating at $\omega$ with mass $m$ and radius $r$?
What is the angular momentum of a disk rotating at $\omega$ with mass $m$ and radius $r$?
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$L = \frac{1}{2}mr^2 \omega$. Uses disk moment of inertia formula.
$L = \frac{1}{2}mr^2 \omega$. Uses disk moment of inertia formula.
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What is the formula for angular acceleration $\alpha$ in terms of $\omega$ and $t$?
What is the formula for angular acceleration $\alpha$ in terms of $\omega$ and $t$?
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$\alpha = \frac{\Delta \omega}{\Delta t}$. Rate of change of angular velocity.
$\alpha = \frac{\Delta \omega}{\Delta t}$. Rate of change of angular velocity.
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What is the effect of external torque on a system's angular momentum?
What is the effect of external torque on a system's angular momentum?
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It changes the angular momentum. Torque causes angular momentum to change over time.
It changes the angular momentum. Torque causes angular momentum to change over time.
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Calculate $L$ for a $1,\text{kg}$ mass moving at $2,\text{m/s}$, $r=1,\text{m}$.
Calculate $L$ for a $1,\text{kg}$ mass moving at $2,\text{m/s}$, $r=1,\text{m}$.
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$L = 2 \text{kg}\cdot\text{m}^2/\text{s}$. Using $L = mvr$: $1 \times 2 \times 1 = 2$.
$L = 2 \text{kg}\cdot\text{m}^2/\text{s}$. Using $L = mvr$: $1 \times 2 \times 1 = 2$.
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Which equation represents the angular impulse-momentum theorem?
Which equation represents the angular impulse-momentum theorem?
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$J = \Delta L$. Angular impulse equals change in angular momentum.
$J = \Delta L$. Angular impulse equals change in angular momentum.
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Which quantity remains constant in an isolated system with no external torque?
Which quantity remains constant in an isolated system with no external torque?
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Angular momentum. Conserved quantity in isolated rotational systems.
Angular momentum. Conserved quantity in isolated rotational systems.
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State the moment of inertia for a solid cylinder.
State the moment of inertia for a solid cylinder.
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$I = \frac{1}{2}mr^2$. Standard formula for solid cylinder rotating about its axis.
$I = \frac{1}{2}mr^2$. Standard formula for solid cylinder rotating about its axis.
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What effect does doubling $m$ have on $L$ if $r$ and $v$ are constant?
What effect does doubling $m$ have on $L$ if $r$ and $v$ are constant?
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$L$ doubles. Angular momentum is proportional to mass.
$L$ doubles. Angular momentum is proportional to mass.
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Calculate the angular impulse given $\tau=5,\text{Nm}$ and $t=3,\text{s}$.
Calculate the angular impulse given $\tau=5,\text{Nm}$ and $t=3,\text{s}$.
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Angular impulse = $15 \text{Nm}\cdot\text{s}$. Simple multiplication: $5 \times 3 = 15$.
Angular impulse = $15 \text{Nm}\cdot\text{s}$. Simple multiplication: $5 \times 3 = 15$.
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What is the unit of angular momentum in SI units?
What is the unit of angular momentum in SI units?
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kg·m²/s. Combines mass (kg), length squared (m²), and time (s).
kg·m²/s. Combines mass (kg), length squared (m²), and time (s).
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Find the change in angular momentum given torque $\tau$ and time $t$.
Find the change in angular momentum given torque $\tau$ and time $t$.
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$\Delta L = \tau \times t$. Angular impulse-momentum theorem application.
$\Delta L = \tau \times t$. Angular impulse-momentum theorem application.
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What is the formula for torque in terms of force and lever arm?
What is the formula for torque in terms of force and lever arm?
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$\tau = rF\sin(\theta)$. Force times perpendicular distance from axis.
$\tau = rF\sin(\theta)$. Force times perpendicular distance from axis.
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State the formula for angular impulse.
State the formula for angular impulse.
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$J = \tau \times \text{time}$. Angular impulse equals torque multiplied by time duration.
$J = \tau \times \text{time}$. Angular impulse equals torque multiplied by time duration.
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What is the moment of inertia for a thin ring?
What is the moment of inertia for a thin ring?
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$I = mr^2$. All mass at distance $r$ from rotation axis.
$I = mr^2$. All mass at distance $r$ from rotation axis.
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What is the formula for angular velocity $\omega$ in terms of period $T$?
What is the formula for angular velocity $\omega$ in terms of period $T$?
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$\omega = \frac{2\pi}{T}$. Relates angular velocity to rotational period.
$\omega = \frac{2\pi}{T}$. Relates angular velocity to rotational period.
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How is angular velocity related to angular momentum?
How is angular velocity related to angular momentum?
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Angular momentum = Moment of inertia × Angular velocity. Angular momentum equals moment of inertia times angular velocity.
Angular momentum = Moment of inertia × Angular velocity. Angular momentum equals moment of inertia times angular velocity.
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What happens to $L$ when radius doubles but mass and velocity remain constant?
What happens to $L$ when radius doubles but mass and velocity remain constant?
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$L$ doubles. Angular momentum is proportional to radius.
$L$ doubles. Angular momentum is proportional to radius.
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Identify the relationship between torque and angular impulse.
Identify the relationship between torque and angular impulse.
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Angular impulse = Torque × Time. Angular impulse is the product of torque and time.
Angular impulse = Torque × Time. Angular impulse is the product of torque and time.
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What happens to $L$ if the direction of velocity is reversed?
What happens to $L$ if the direction of velocity is reversed?
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$L$ reverses direction. Angular momentum is a vector quantity.
$L$ reverses direction. Angular momentum is a vector quantity.
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What is the primary cause of a change in angular momentum?
What is the primary cause of a change in angular momentum?
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External torque. Torque is the rotational analog of force.
External torque. Torque is the rotational analog of force.
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