Angular Momentum and Angular Impulse - AP Physics C: Mechanics
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What is the formula for the moment of inertia of a thin rod about its center?
What is the formula for the moment of inertia of a thin rod about its center?
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$I = \frac{1}{12}ml^2$. Standard moment of inertia for uniform thin rod.
$I = \frac{1}{12}ml^2$. Standard moment of inertia for uniform thin rod.
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What is the formula for angular momentum of a particle?
What is the formula for angular momentum of a particle?
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$L = r \times p = r \times mv$. Cross product of position and linear momentum vectors.
$L = r \times p = r \times mv$. Cross product of position and linear momentum vectors.
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Identify the symbol for angular momentum.
Identify the symbol for angular momentum.
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$L$. Standard physics symbol for angular momentum quantity.
$L$. Standard physics symbol for angular momentum quantity.
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State the principle of angular momentum conservation.
State the principle of angular momentum conservation.
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Angular momentum is conserved in the absence of external torques. Fundamental law for isolated rotational systems.
Angular momentum is conserved in the absence of external torques. Fundamental law for isolated rotational systems.
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State the formula for torque in terms of force and lever arm.
State the formula for torque in terms of force and lever arm.
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$\tau = r \times F \times \text{sin}(\theta)$. Perpendicular distance from axis multiplied by force component.
$\tau = r \times F \times \text{sin}(\theta)$. Perpendicular distance from axis multiplied by force component.
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State the conservation of angular momentum principle.
State the conservation of angular momentum principle.
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Total angular momentum is constant if net external torque is zero. Fundamental principle for rotational systems without external torques.
Total angular momentum is constant if net external torque is zero. Fundamental principle for rotational systems without external torques.
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How is angular momentum affected by a perpendicular force?
How is angular momentum affected by a perpendicular force?
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It causes a change in angular momentum. Perpendicular force creates torque, changing angular momentum.
It causes a change in angular momentum. Perpendicular force creates torque, changing angular momentum.
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State the formula for torque in terms of force and lever arm.
State the formula for torque in terms of force and lever arm.
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$\tau = r \times F \times \text{sin}(\theta)$. Perpendicular distance from axis multiplied by force component.
$\tau = r \times F \times \text{sin}(\theta)$. Perpendicular distance from axis multiplied by force component.
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Find angular momentum of a 3 kg particle moving at 2 m/s, radius 4 m.
Find angular momentum of a 3 kg particle moving at 2 m/s, radius 4 m.
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$L = 24 \text{ kg}\text{m}^2/\text{s}$. Using $L = mvr$: $3 \times 2 \times 4 = 24$.
$L = 24 \text{ kg}\text{m}^2/\text{s}$. Using $L = mvr$: $3 \times 2 \times 4 = 24$.
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State the principle of angular momentum conservation.
State the principle of angular momentum conservation.
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Angular momentum is conserved in the absence of external torques. Fundamental law for isolated rotational systems.
Angular momentum is conserved in the absence of external torques. Fundamental law for isolated rotational systems.
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Identify the symbol for angular momentum.
Identify the symbol for angular momentum.
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$L$. Standard physics symbol for angular momentum quantity.
$L$. Standard physics symbol for angular momentum quantity.
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Calculate angular momentum for a mass of 2 kg at 4 m/s, radius 1 m.
Calculate angular momentum for a mass of 2 kg at 4 m/s, radius 1 m.
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$L = 8 \text{ kg}\text{m}^2/\text{s}$. Apply formula: $L = mvr = 2 \times 4 \times 1 = 8$.
$L = 8 \text{ kg}\text{m}^2/\text{s}$. Apply formula: $L = mvr = 2 \times 4 \times 1 = 8$.
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What is the formula for the moment of inertia of a thin rod about its center?
What is the formula for the moment of inertia of a thin rod about its center?
Tap to reveal answer
$I = \frac{1}{12}ml^2$. Standard moment of inertia for uniform thin rod.
$I = \frac{1}{12}ml^2$. Standard moment of inertia for uniform thin rod.
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What is the formula for angular momentum of a particle?
What is the formula for angular momentum of a particle?
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$L = r \times p = r \times mv$. Cross product of position and linear momentum vectors.
$L = r \times p = r \times mv$. Cross product of position and linear momentum vectors.
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What is the effect of applying a net torque on a system?
What is the effect of applying a net torque on a system?
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It changes the angular momentum. Net torque causes angular momentum to change over time.
It changes the angular momentum. Net torque causes angular momentum to change over time.
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Identify the units of torque.
Identify the units of torque.
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Newton meter (Nm). Standard SI unit for torque, equivalent to kg⋅m²⋅s⁻².
Newton meter (Nm). Standard SI unit for torque, equivalent to kg⋅m²⋅s⁻².
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What is the effect of a constant external torque on a system?
What is the effect of a constant external torque on a system?
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It results in a constant change in angular momentum. Constant torque produces linear change in angular momentum.
It results in a constant change in angular momentum. Constant torque produces linear change in angular momentum.
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State the conservation of angular momentum principle.
State the conservation of angular momentum principle.
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Total angular momentum is constant if net external torque is zero. Fundamental principle for rotational systems without external torques.
Total angular momentum is constant if net external torque is zero. Fundamental principle for rotational systems without external torques.
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Calculate angular impulse if torque is 5 Nm over 3 s.
Calculate angular impulse if torque is 5 Nm over 3 s.
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$J = 15 \text{ Nms}$. Angular impulse equals torque times time interval.
$J = 15 \text{ Nms}$. Angular impulse equals torque times time interval.
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If net external torque is zero, what happens to angular momentum?
If net external torque is zero, what happens to angular momentum?
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It remains constant. Conservation of angular momentum applies when $\tau_{ext} = 0$.
It remains constant. Conservation of angular momentum applies when $\tau_{ext} = 0$.
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Determine the change in angular momentum for a 10 Nm torque applied for 5 s.
Determine the change in angular momentum for a 10 Nm torque applied for 5 s.
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$\triangle L = 50 \text{ Nms}$. Apply $\triangle L = \tau \triangle t$: $10 \times 5 = 50$.
$\triangle L = 50 \text{ Nms}$. Apply $\triangle L = \tau \triangle t$: $10 \times 5 = 50$.
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What determines the direction of angular momentum?
What determines the direction of angular momentum?
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The right-hand rule. Curl fingers with rotation, thumb points in $\vec{L}$ direction.
The right-hand rule. Curl fingers with rotation, thumb points in $\vec{L}$ direction.
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How is angular momentum conserved in an isolated system?
How is angular momentum conserved in an isolated system?
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No external torque implies constant angular momentum. Zero net external torque ensures angular momentum conservation.
No external torque implies constant angular momentum. Zero net external torque ensures angular momentum conservation.
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Find the angular momentum of a 5 kg mass at 3 m/s, radius 2 m.
Find the angular momentum of a 5 kg mass at 3 m/s, radius 2 m.
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$L = 30 \text{ kg}\text{m}^2/\text{s}$. Calculate: $L = mvr = 5 \times 3 \times 2 = 30$.
$L = 30 \text{ kg}\text{m}^2/\text{s}$. Calculate: $L = mvr = 5 \times 3 \times 2 = 30$.
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How is angular momentum affected by a perpendicular force?
How is angular momentum affected by a perpendicular force?
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It causes a change in angular momentum. Perpendicular force creates torque, changing angular momentum.
It causes a change in angular momentum. Perpendicular force creates torque, changing angular momentum.
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State the equation relating angular impulse and change in angular momentum.
State the equation relating angular impulse and change in angular momentum.
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$J = \triangle L$. Angular impulse equals the change in angular momentum.
$J = \triangle L$. Angular impulse equals the change in angular momentum.
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What is the moment of inertia for a solid sphere?
What is the moment of inertia for a solid sphere?
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$I = \frac{2}{5}mr^2$. Standard moment of inertia formula for uniform solid sphere.
$I = \frac{2}{5}mr^2$. Standard moment of inertia formula for uniform solid sphere.
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Calculate the change in angular momentum for $\tau = 6 \text{ Nm}$ over $t = 4 \text{ s}$.
Calculate the change in angular momentum for $\tau = 6 \text{ Nm}$ over $t = 4 \text{ s}$.
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$\triangle L = 24 \text{ Nms}$. Apply impulse formula: $\triangle L = \tau \triangle t = 6 \times 4 = 24$.
$\triangle L = 24 \text{ Nms}$. Apply impulse formula: $\triangle L = \tau \triangle t = 6 \times 4 = 24$.
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What happens to angular momentum if no external torques act?
What happens to angular momentum if no external torques act?
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It remains constant. Angular momentum conservation when no external torques present.
It remains constant. Angular momentum conservation when no external torques present.
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Find angular momentum of a 3 kg particle moving at 2 m/s, radius 4 m.
Find angular momentum of a 3 kg particle moving at 2 m/s, radius 4 m.
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$L = 24 \text{ kg}\text{m}^2/\text{s}$. Using $L = mvr$: $3 \times 2 \times 4 = 24$.
$L = 24 \text{ kg}\text{m}^2/\text{s}$. Using $L = mvr$: $3 \times 2 \times 4 = 24$.
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