Rotational Inertia - AP Physics C: Mechanics
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Which factor does not affect rotational inertia?
Which factor does not affect rotational inertia?
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Color of the object. Rotational inertia depends only on mass distribution and geometry.
Color of the object. Rotational inertia depends only on mass distribution and geometry.
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Which object has higher rotational inertia: hoop or solid disk of same mass and radius?
Which object has higher rotational inertia: hoop or solid disk of same mass and radius?
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Hoop. Hoop has all mass at maximum radius from center.
Hoop. Hoop has all mass at maximum radius from center.
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What happens to rotational inertia if mass is doubled?
What happens to rotational inertia if mass is doubled?
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Rotational inertia doubles. Rotational inertia is directly proportional to mass.
Rotational inertia doubles. Rotational inertia is directly proportional to mass.
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What is the effect of increasing radius on rotational inertia?
What is the effect of increasing radius on rotational inertia?
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Rotational inertia increases. Inertia depends on $R^2$ in most formulas.
Rotational inertia increases. Inertia depends on $R^2$ in most formulas.
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Calculate the rotational inertia for a 2 kg point mass 3 m from the axis.
Calculate the rotational inertia for a 2 kg point mass 3 m from the axis.
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$I = 18 \text{ kg m}^2$. Using $I = mr^2$ with $m=2$ kg, $r=3$ m.
$I = 18 \text{ kg m}^2$. Using $I = mr^2$ with $m=2$ kg, $r=3$ m.
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Calculate the rotational inertia of a 3 kg disk, radius 0.4 m, about its center.
Calculate the rotational inertia of a 3 kg disk, radius 0.4 m, about its center.
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$I = 0.24 \text{ kg m}^2$. Using solid disk formula $I = \frac{1}{2}MR^2$.
$I = 0.24 \text{ kg m}^2$. Using solid disk formula $I = \frac{1}{2}MR^2$.
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Find rotational inertia of a 4 kg hoop, radius 0.7 m, about its center.
Find rotational inertia of a 4 kg hoop, radius 0.7 m, about its center.
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$I = 1.96 \text{ kg m}^2$. Using hoop formula $I = MR^2$ with given values.
$I = 1.96 \text{ kg m}^2$. Using hoop formula $I = MR^2$ with given values.
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Identify the variable representing radius in rotational inertia formulas.
Identify the variable representing radius in rotational inertia formulas.
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$R$. Radius determines distance from rotation axis.
$R$. Radius determines distance from rotation axis.
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What is the formula for rotational inertia of a thin spherical shell?
What is the formula for rotational inertia of a thin spherical shell?
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$I = \frac{2}{3} MR^2$. All mass located at the spherical surface.
$I = \frac{2}{3} MR^2$. All mass located at the spherical surface.
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State the formula for rotational inertia of a hoop about its center.
State the formula for rotational inertia of a hoop about its center.
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$I = MR^2$. All mass concentrated at maximum distance from center.
$I = MR^2$. All mass concentrated at maximum distance from center.
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What is the unit of rotational inertia in the SI system?
What is the unit of rotational inertia in the SI system?
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Kilogram meter squared ($\text{kg m}^2$). Derived from $[M][L]^2$ dimensional analysis.
Kilogram meter squared ($\text{kg m}^2$). Derived from $[M][L]^2$ dimensional analysis.
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Find the rotational inertia of a 5 kg solid sphere with radius 0.5 m.
Find the rotational inertia of a 5 kg solid sphere with radius 0.5 m.
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$I = 0.5 \text{ kg m}^2$. Using solid sphere formula with given values.
$I = 0.5 \text{ kg m}^2$. Using solid sphere formula with given values.
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What is the parallel axis theorem formula?
What is the parallel axis theorem formula?
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$I = I_c + Md^2$. Relates inertia about parallel axes to center-of-mass inertia.
$I = I_c + Md^2$. Relates inertia about parallel axes to center-of-mass inertia.
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What is rotational inertia's role in angular motion?
What is rotational inertia's role in angular motion?
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It resists changes in angular velocity. Rotational analog of mass in linear motion.
It resists changes in angular velocity. Rotational analog of mass in linear motion.
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Calculate torque for a rotational inertia of 2 kg m² and angular acceleration 4 rad/s².
Calculate torque for a rotational inertia of 2 kg m² and angular acceleration 4 rad/s².
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$\tau = 8 \text{ Nm}$. Using $\tau = I\alpha$ with given values.
$\tau = 8 \text{ Nm}$. Using $\tau = I\alpha$ with given values.
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What is the effect of rotational inertia on rolling motion?
What is the effect of rotational inertia on rolling motion?
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Higher inertia slows acceleration. Greater inertia requires more torque for same acceleration.
Higher inertia slows acceleration. Greater inertia requires more torque for same acceleration.
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Calculate rotational inertia of a 8 kg hollow sphere, radius 0.3 m, about its center.
Calculate rotational inertia of a 8 kg hollow sphere, radius 0.3 m, about its center.
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$I = 0.48 \text{ kg m}^2$. Using hollow sphere formula with given values.
$I = 0.48 \text{ kg m}^2$. Using hollow sphere formula with given values.
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What is rotational inertia of a uniform rod about its center?
What is rotational inertia of a uniform rod about its center?
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$I = \frac{1}{12} ML^2$. Rod rotates about perpendicular axis through center.
$I = \frac{1}{12} ML^2$. Rod rotates about perpendicular axis through center.
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How does increasing mass affect rotational inertia?
How does increasing mass affect rotational inertia?
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Directly increases. Rotational inertia is linearly proportional to mass.
Directly increases. Rotational inertia is linearly proportional to mass.
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Identify the dependency of rotational inertia on shape.
Identify the dependency of rotational inertia on shape.
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Depends on the mass distribution. Different shapes have different inertia formulas.
Depends on the mass distribution. Different shapes have different inertia formulas.
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Find rotational inertia of a 6 kg rod, length 2 m, about its center.
Find rotational inertia of a 6 kg rod, length 2 m, about its center.
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$I = 2 , \text{kg} , \mathrm{m^2}$. Using rod formula $I = \frac{1}{12}ML^2$ about center.
$I = 2 , \text{kg} , \mathrm{m^2}$. Using rod formula $I = \frac{1}{12}ML^2$ about center.
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What is the formula for rotational inertia of a solid cylinder?
What is the formula for rotational inertia of a solid cylinder?
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$I = \frac{1}{2} MR^2$. For solid cylinder rotating about central axis.
$I = \frac{1}{2} MR^2$. For solid cylinder rotating about central axis.
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What happens to inertia when the axis of rotation is changed?
What happens to inertia when the axis of rotation is changed?
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It may increase or decrease. Inertia depends on distance from specific rotation axis.
It may increase or decrease. Inertia depends on distance from specific rotation axis.
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Find rotational inertia of a 6 kg rod, length 2 m, about its center.
Find rotational inertia of a 6 kg rod, length 2 m, about its center.
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$I = 2 \text{ kg m}^2$. Using rod formula $I = \frac{1}{12}ML^2$ about center.
$I = 2 \text{ kg m}^2$. Using rod formula $I = \frac{1}{12}ML^2$ about center.
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What is the rotational inertia of a point mass $m$ at distance $r$ from axis?
What is the rotational inertia of a point mass $m$ at distance $r$ from axis?
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$I = mr^2$. Fundamental definition for point mass rotational inertia.
$I = mr^2$. Fundamental definition for point mass rotational inertia.
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State the formula for rotational inertia of a thin rod about its end.
State the formula for rotational inertia of a thin rod about its end.
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$I = \frac{1}{3} ML^2$. Rod pivots about one end, maximizing distance from axis.
$I = \frac{1}{3} ML^2$. Rod pivots about one end, maximizing distance from axis.
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What is the formula for rotational inertia of a solid sphere?
What is the formula for rotational inertia of a solid sphere?
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$I = \frac{2}{5} MR^2$. Mass distributed throughout sphere's volume.
$I = \frac{2}{5} MR^2$. Mass distributed throughout sphere's volume.
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State the formula for rotational inertia of a hollow sphere.
State the formula for rotational inertia of a hollow sphere.
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$I = \frac{2}{3} MR^2$. All mass concentrated at surface of sphere.
$I = \frac{2}{3} MR^2$. All mass concentrated at surface of sphere.
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What is the formula for rotational inertia of a thin spherical shell?
What is the formula for rotational inertia of a thin spherical shell?
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$I = \frac{2}{3} MR^2$. All mass located at the spherical surface.
$I = \frac{2}{3} MR^2$. All mass located at the spherical surface.
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State the formula for rotational inertia of a hoop about its center.
State the formula for rotational inertia of a hoop about its center.
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$I = MR^2$. All mass concentrated at maximum distance from center.
$I = MR^2$. All mass concentrated at maximum distance from center.
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