Rolling - AP Physics 1
Card 1 of 30
What is the formula for the work done by torque on a rolling object?
What is the formula for the work done by torque on a rolling object?
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$W = \tau \theta$. Work equals torque times angular displacement.
$W = \tau \theta$. Work equals torque times angular displacement.
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What is the equation for the translational kinetic energy of a rolling object?
What is the equation for the translational kinetic energy of a rolling object?
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$KE_{\text{trans}} = \frac{1}{2} mv^2$. Translational KE depends on mass and linear velocity squared.
$KE_{\text{trans}} = \frac{1}{2} mv^2$. Translational KE depends on mass and linear velocity squared.
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What is the moment of inertia of a hollow cylinder rolling about its central axis?
What is the moment of inertia of a hollow cylinder rolling about its central axis?
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$I = m r^2$. For a thin-walled cylinder, all mass is at radius $r$.
$I = m r^2$. For a thin-walled cylinder, all mass is at radius $r$.
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What is the condition for rolling without slipping?
What is the condition for rolling without slipping?
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$v = r \theta$. For no slipping, contact point velocity equals zero.
$v = r \theta$. For no slipping, contact point velocity equals zero.
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What is the expression for the angular displacement of a rolling object?
What is the expression for the angular displacement of a rolling object?
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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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Find the rolling distance given angular displacement $\theta$ and radius $r$.
Find the rolling distance given angular displacement $\theta$ and radius $r$.
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$s = r \theta$. Rolling distance equals radius times angular displacement.
$s = r \theta$. Rolling distance equals radius times angular displacement.
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What is the formula for the moment of inertia of a solid cylinder rolling about its central axis?
What is the formula for the moment of inertia of a solid cylinder rolling about its central axis?
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$I = \frac{1}{2} m r^2$. For a solid cylinder, moment of inertia equals half mass times radius squared.
$I = \frac{1}{2} m r^2$. For a solid cylinder, moment of inertia equals half mass times radius squared.
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State the formula for the total mechanical energy of a rolling object.
State the formula for the total mechanical energy of a rolling object.
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$E = KE_{\text{trans}} + KE_{\text{rot}}$. Total energy is the sum of translational and rotational kinetic energies.
$E = KE_{\text{trans}} + KE_{\text{rot}}$. Total energy is the sum of translational and rotational kinetic energies.
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What is the formula for the centripetal force on a rolling object?
What is the formula for the centripetal force on a rolling object?
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$F_c = \frac{mv^2}{r}$. Centripetal force equals mass times velocity squared over radius.
$F_c = \frac{mv^2}{r}$. Centripetal force equals mass times velocity squared over radius.
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What is the moment of inertia for a thin spherical shell rolling about its central axis?
What is the moment of inertia for a thin spherical shell rolling about its central axis?
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$I = \frac{2}{3} m r^2$. For a hollow sphere, $I$ is two-thirds of $mr^2$.
$I = \frac{2}{3} m r^2$. For a hollow sphere, $I$ is two-thirds of $mr^2$.
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What is the formula for potential energy of a rolling object at height $h$?
What is the formula for potential energy of a rolling object at height $h$?
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$PE = mgh$. Gravitational potential energy depends on mass, gravity, and height.
$PE = mgh$. Gravitational potential energy depends on mass, gravity, and height.
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What is the moment of inertia for a solid sphere rolling about its central axis?
What is the moment of inertia for a solid sphere rolling about its central axis?
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$I = \frac{2}{5} m r^2$. For a solid sphere, $I$ is two-fifths of $mr^2$.
$I = \frac{2}{5} m r^2$. For a solid sphere, $I$ is two-fifths of $mr^2$.
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Calculate the moment of inertia for a ring rolling about its central axis.
Calculate the moment of inertia for a ring rolling about its central axis.
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$I = m r^2$. For a thin ring, all mass is concentrated at radius $r$.
$I = m r^2$. For a thin ring, all mass is concentrated at radius $r$.
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What is the condition for rolling without slipping?
What is the condition for rolling without slipping?
Tap to reveal answer
$v = r \theta$. For no slipping, contact point velocity equals zero.
$v = r \theta$. For no slipping, contact point velocity equals zero.
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What is the moment of inertia for a solid sphere rolling about its central axis?
What is the moment of inertia for a solid sphere rolling about its central axis?
Tap to reveal answer
$I = \frac{2}{5} m r^2$. For a solid sphere, $I$ is two-fifths of $mr^2$.
$I = \frac{2}{5} m r^2$. For a solid sphere, $I$ is two-fifths of $mr^2$.
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State the formula for the total mechanical energy of a rolling object.
State the formula for the total mechanical energy of a rolling object.
Tap to reveal answer
$E = KE_{\text{trans}} + KE_{\text{rot}}$. Total energy is the sum of translational and rotational kinetic energies.
$E = KE_{\text{trans}} + KE_{\text{rot}}$. Total energy is the sum of translational and rotational kinetic energies.
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What is the moment of inertia of a hollow cylinder rolling about its central axis?
What is the moment of inertia of a hollow cylinder rolling about its central axis?
Tap to reveal answer
$I = m r^2$. For a thin-walled cylinder, all mass is at radius $r$.
$I = m r^2$. For a thin-walled cylinder, all mass is at radius $r$.
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What is the formula for the work done by torque on a rolling object?
What is the formula for the work done by torque on a rolling object?
Tap to reveal answer
$W = \tau \theta$. Work equals torque times angular displacement.
$W = \tau \theta$. Work equals torque times angular displacement.
← Didn't Know|Knew It →
Calculate the moment of inertia for a ring rolling about its central axis.
Calculate the moment of inertia for a ring rolling about its central axis.
Tap to reveal answer
$I = m r^2$. For a thin ring, all mass is concentrated at radius $r$.
$I = m r^2$. For a thin ring, all mass is concentrated at radius $r$.
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Find the rolling distance given angular displacement $\theta$ and radius $r$.
Find the rolling distance given angular displacement $\theta$ and radius $r$.
Tap to reveal answer
$s = r \theta$. Rolling distance equals radius times angular displacement.
$s = r \theta$. Rolling distance equals radius times angular displacement.
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What is the expression for the angular displacement of a rolling object?
What is the expression for the angular displacement of a rolling object?
Tap to reveal answer
$\theta = \frac{s}{r}$. Angular displacement equals arc length divided by radius.
$\theta = \frac{s}{r}$. Angular displacement equals arc length divided by radius.
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What is the formula for potential energy of a rolling object at height $h$?
What is the formula for potential energy of a rolling object at height $h$?
Tap to reveal answer
$PE = mgh$. Gravitational potential energy depends on mass, gravity, and height.
$PE = mgh$. Gravitational potential energy depends on mass, gravity, and height.
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What is the moment of inertia for a thin spherical shell rolling about its central axis?
What is the moment of inertia for a thin spherical shell rolling about its central axis?
Tap to reveal answer
$I = \frac{2}{3} m r^2$. For a hollow sphere, $I$ is two-thirds of $mr^2$.
$I = \frac{2}{3} m r^2$. For a hollow sphere, $I$ is two-thirds of $mr^2$.
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What is the equation for the translational kinetic energy of a rolling object?
What is the equation for the translational kinetic energy of a rolling object?
Tap to reveal answer
$KE_{\text{trans}} = \frac{1}{2} mv^2$. Translational KE depends on mass and linear velocity squared.
$KE_{\text{trans}} = \frac{1}{2} mv^2$. Translational KE depends on mass and linear velocity squared.
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What is the formula for the centripetal force on a rolling object?
What is the formula for the centripetal force on a rolling object?
Tap to reveal answer
$F_c = \frac{mv^2}{r}$. Centripetal force equals mass times velocity squared over radius.
$F_c = \frac{mv^2}{r}$. Centripetal force equals mass times velocity squared over radius.
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What is the formula for the moment of inertia of a solid cylinder rolling about its central axis?
What is the formula for the moment of inertia of a solid cylinder rolling about its central axis?
Tap to reveal answer
$I = \frac{1}{2} m r^2$. For a solid cylinder, moment of inertia equals half mass times radius squared.
$I = \frac{1}{2} m r^2$. For a solid cylinder, moment of inertia equals half mass times radius squared.
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What is the rolling-without-slipping condition relating $v_{cm}$ and $\omega$ for radius $R$?
What is the rolling-without-slipping condition relating $v_{cm}$ and $\omega$ for radius $R$?
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$v_{cm}=\omega R$. Center of mass velocity equals angular velocity times radius for pure rolling.
$v_{cm}=\omega R$. Center of mass velocity equals angular velocity times radius for pure rolling.
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What is the parallel-axis theorem for moment of inertia?
What is the parallel-axis theorem for moment of inertia?
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$I=I_{cm}+md^2$. Relates moment of inertia about any axis to that about center of mass.
$I=I_{cm}+md^2$. Relates moment of inertia about any axis to that about center of mass.
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What is the speed of a point on the rim at the top of a rolling wheel (relative to ground)?
What is the speed of a point on the rim at the top of a rolling wheel (relative to ground)?
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$v_{top}=2v_{cm}$. Top point moves at $v_{cm}$ plus rim speed $\omega R = v_{cm}$.
$v_{top}=2v_{cm}$. Top point moves at $v_{cm}$ plus rim speed $\omega R = v_{cm}$.
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What is the instantaneous speed of the contact point on a rolling wheel (relative to ground)?
What is the instantaneous speed of the contact point on a rolling wheel (relative to ground)?
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$v_{contact}=0$. Contact point is instantaneous center of rotation for pure rolling.
$v_{contact}=0$. Contact point is instantaneous center of rotation for pure rolling.
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