Connecting Linear and Rotational Motion - AP Physics C: Mechanics
Card 1 of 30
State the relationship between rotational and translational kinetic energy.
State the relationship between rotational and translational kinetic energy.
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$KE_{total} = KE_{trans} + KE_{rot}$. Total kinetic energy is sum of translational and rotational parts.
$KE_{total} = KE_{trans} + KE_{rot}$. Total kinetic energy is sum of translational and rotational parts.
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Find the moment of inertia for a hoop of mass $M$ and radius $R$.
Find the moment of inertia for a hoop of mass $M$ and radius $R$.
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$I = MR^2$. For a hoop, all mass is at radius $R$ from center.
$I = MR^2$. For a hoop, all mass is at radius $R$ from center.
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Calculate the frequency if angular velocity is $4\text{π} \text{ rad/s}$.
Calculate the frequency if angular velocity is $4\text{π} \text{ rad/s}$.
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$f = 2 \text{ Hz}$. Use $f = \frac{\omega}{2\pi} = \frac{4\pi}{2\pi} = 2$ Hz.
$f = 2 \text{ Hz}$. Use $f = \frac{\omega}{2\pi} = \frac{4\pi}{2\pi} = 2$ Hz.
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What is the unit of angular displacement in the SI system?
What is the unit of angular displacement in the SI system?
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radians (rad). Angular displacement measures rotation angle in radians.
radians (rad). Angular displacement measures rotation angle in radians.
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Calculate the period if angular frequency is $6\text{π} \text{ rad/s}$.
Calculate the period if angular frequency is $6\text{π} \text{ rad/s}$.
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$T = \frac{1}{3} \text{ s}$. Use $T = \frac{2\pi}{\omega} = \frac{2\pi}{6\pi} = \frac{1}{3}$ s.
$T = \frac{1}{3} \text{ s}$. Use $T = \frac{2\pi}{\omega} = \frac{2\pi}{6\pi} = \frac{1}{3}$ s.
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What is the formula for the moment of inertia of a point mass?
What is the formula for the moment of inertia of a point mass?
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$I = mr^2$. Point mass inertia is mass times radius squared.
$I = mr^2$. Point mass inertia is mass times radius squared.
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Identify the unit of angular velocity in the SI system.
Identify the unit of angular velocity in the SI system.
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radians per second (rad/s). Angular velocity measures rotation rate in radians per time.
radians per second (rad/s). Angular velocity measures rotation rate in radians per time.
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State the formula for the angular displacement in terms of linear displacement.
State the formula for the angular displacement in terms of linear displacement.
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$\theta = \frac{s}{r}$. Angular displacement equals arc length divided by radius.
$\theta = \frac{s}{r}$. Angular displacement equals arc length divided by radius.
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Identify the rotational counterpart of force in linear motion.
Identify the rotational counterpart of force in linear motion.
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Torque. Torque causes rotational motion like force causes linear motion.
Torque. Torque causes rotational motion like force causes linear motion.
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What is the formula for torque?
What is the formula for torque?
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$\tau = rF\text{sin}(\theta)$. Torque equals perpendicular force times lever arm distance.
$\tau = rF\text{sin}(\theta)$. Torque equals perpendicular force times lever arm distance.
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State the formula for the conservation of angular momentum.
State the formula for the conservation of angular momentum.
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$L_i = L_f$. Angular momentum is conserved when no external torque acts.
$L_i = L_f$. Angular momentum is conserved when no external torque acts.
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What is the formula for linear displacement in terms of angular displacement?
What is the formula for linear displacement in terms of angular displacement?
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$s = r\theta$. Arc length equals radius times angular displacement.
$s = r\theta$. Arc length equals radius times angular displacement.
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Find the angular displacement if $s = 8 \text{ m}$ and $r = 2 \text{ m}$.
Find the angular displacement if $s = 8 \text{ m}$ and $r = 2 \text{ m}$.
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$\theta = 4 \text{ rad}$. Use $\theta = \frac{s}{r} = \frac{8}{2} = 4$ rad.
$\theta = 4 \text{ rad}$. Use $\theta = \frac{s}{r} = \frac{8}{2} = 4$ rad.
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Identify the rotational counterpart of mass in linear motion.
Identify the rotational counterpart of mass in linear motion.
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Moment of Inertia. Moment of inertia resists rotational motion like mass resists linear motion.
Moment of Inertia. Moment of inertia resists rotational motion like mass resists linear motion.
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Calculate the torque with $F = 10 \text{ N}$, $r = 0.5 \text{ m}$, and angle $90^\text{o}$.
Calculate the torque with $F = 10 \text{ N}$, $r = 0.5 \text{ m}$, and angle $90^\text{o}$.
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$\tau = 5 \text{ Nm}$. Use $\tau = rF\sin(90°) = 0.5 \times 10 \times 1 = 5$ Nm.
$\tau = 5 \text{ Nm}$. Use $\tau = rF\sin(90°) = 0.5 \times 10 \times 1 = 5$ Nm.
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What is the unit of torque in the SI system?
What is the unit of torque in the SI system?
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Newton meter (Nm). Torque has units of force times distance.
Newton meter (Nm). Torque has units of force times distance.
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What is the unit of angular displacement in the SI system?
What is the unit of angular displacement in the SI system?
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radians (rad). Angular displacement measures rotation angle in radians.
radians (rad). Angular displacement measures rotation angle in radians.
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Identify the rotational counterpart of force in linear motion.
Identify the rotational counterpart of force in linear motion.
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Torque. Torque causes rotational motion like force causes linear motion.
Torque. Torque causes rotational motion like force causes linear motion.
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What is the formula for torque?
What is the formula for torque?
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$\tau = rF\text{sin}(\theta)$. Torque equals perpendicular force times lever arm distance.
$\tau = rF\text{sin}(\theta)$. Torque equals perpendicular force times lever arm distance.
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What is the formula for linear displacement in terms of angular displacement?
What is the formula for linear displacement in terms of angular displacement?
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$s = r\theta$. Arc length equals radius times angular displacement.
$s = r\theta$. Arc length equals radius times angular displacement.
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Find the angular displacement if $s = 8 \text{ m}$ and $r = 2 \text{ m}$.
Find the angular displacement if $s = 8 \text{ m}$ and $r = 2 \text{ m}$.
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$\theta = 4 \text{ rad}$. Use $\theta = \frac{s}{r} = \frac{8}{2} = 4$ rad.
$\theta = 4 \text{ rad}$. Use $\theta = \frac{s}{r} = \frac{8}{2} = 4$ rad.
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Calculate the torque with $F = 10 \text{ N}$, $r = 0.5 \text{ m}$, and angle $90^\text{o}$.
Calculate the torque with $F = 10 \text{ N}$, $r = 0.5 \text{ m}$, and angle $90^\text{o}$.
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$\tau = 5 \text{ Nm}$. Use $\tau = rF\sin(90°) = 0.5 \times 10 \times 1 = 5$ Nm.
$\tau = 5 \text{ Nm}$. Use $\tau = rF\sin(90°) = 0.5 \times 10 \times 1 = 5$ Nm.
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What is the unit of torque in the SI system?
What is the unit of torque in the SI system?
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Newton meter (Nm). Torque has units of force times distance.
Newton meter (Nm). Torque has units of force times distance.
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State the relationship between rotational and translational kinetic energy.
State the relationship between rotational and translational kinetic energy.
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$KE_{total} = KE_{trans} + KE_{rot}$. Total kinetic energy is sum of translational and rotational parts.
$KE_{total} = KE_{trans} + KE_{rot}$. Total kinetic energy is sum of translational and rotational parts.
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Find the moment of inertia for a hoop of mass $M$ and radius $R$.
Find the moment of inertia for a hoop of mass $M$ and radius $R$.
Tap to reveal answer
$I = MR^2$. For a hoop, all mass is at radius $R$ from center.
$I = MR^2$. For a hoop, all mass is at radius $R$ from center.
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Identify the rotational counterpart of mass in linear motion.
Identify the rotational counterpart of mass in linear motion.
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Moment of Inertia. Moment of inertia resists rotational motion like mass resists linear motion.
Moment of Inertia. Moment of inertia resists rotational motion like mass resists linear motion.
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State the formula for the angular displacement in terms of linear displacement.
State the formula for the angular displacement in terms of linear displacement.
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$\theta = \frac{s}{r}$. Angular displacement equals arc length divided by radius.
$\theta = \frac{s}{r}$. Angular displacement equals arc length divided by radius.
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Calculate the period if angular frequency is $6\text{π} \text{ rad/s}$.
Calculate the period if angular frequency is $6\text{π} \text{ rad/s}$.
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$T = \frac{1}{3} \text{ s}$. Use $T = \frac{2\pi}{\omega} = \frac{2\pi}{6\pi} = \frac{1}{3}$ s.
$T = \frac{1}{3} \text{ s}$. Use $T = \frac{2\pi}{\omega} = \frac{2\pi}{6\pi} = \frac{1}{3}$ s.
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Identify the unit of angular velocity in the SI system.
Identify the unit of angular velocity in the SI system.
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radians per second (rad/s). Angular velocity measures rotation rate in radians per time.
radians per second (rad/s). Angular velocity measures rotation rate in radians per time.
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State the formula for the conservation of angular momentum.
State the formula for the conservation of angular momentum.
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$L_i = L_f$. Angular momentum is conserved when no external torque acts.
$L_i = L_f$. Angular momentum is conserved when no external torque acts.
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