AP Physics 1 Quiz: Rotational Kinetic Energy

20 questions · exam conditions

0:00

Rotational Kinetic EnergyQuestion 1 of 20

Two objects rotate about fixed axes with the same angular speed $\omega$ . Object X has a larger moment of inertia than Object Y about its axis. Which statement about rotational kinetic energy is correct?

Object Y has greater rotational kinetic energy because it is easier to spin.

They have equal rotational kinetic energy because

\omega

is the same.

Object X has greater rotational kinetic energy because

K_{\text{rot}}\propto I

for fixed

\omega

Their rotational kinetic energies depend only on mass, not on

I

← Back to quizzes

AP Physics 1 Quiz

AP Physics 1 Quiz: Rotational Kinetic Energy

Practice Rotational Kinetic Energy in AP Physics 1 with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Rotational Kinetic Energy, giving you a quick way to practice the rules, question types, and explanations that matter most for AP Physics 1.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

All questions

Question 1

Object Y has greater rotational kinetic energy because it is easier to spin.
They have equal rotational kinetic energy because $\omega$ is the same.
Object X has greater rotational kinetic energy because $K_{\text{rot}}\propto I$ for fixed $\omega$ . (correct answer)
Their rotational kinetic energies depend only on mass, not on $I$ .

Explanation: This question tests understanding of rotational kinetic energy. Rotational kinetic energy is given by K_rot = ½Iω², showing linear dependence on moment of inertia I and quadratic dependence on angular speed ω. Since both objects rotate at the same angular speed ω, their rotational kinetic energies differ only due to their different moments of inertia. Object X has larger I, so K_rot,X = ½I_Xω² > K_rot,Y = ½I_Yω², meaning Object X has greater rotational kinetic energy. Choice A incorrectly associates "easier to spin" (lower I) with greater kinetic energy, when the opposite is true for fixed ω. When comparing rotational kinetic energies at equal angular speeds, the object with larger moment of inertia has more rotational kinetic energy.

Question 2

A rigid object rotates about a fixed axis with angular speed $\omega$ . A second object has the same mass but smaller moment of inertia about its axis and rotates at the same $\omega$ . Which statement is correct?

They have equal rotational kinetic energy because their masses are equal.
The second object has greater rotational kinetic energy because smaller $I$ means larger energy.
The first object has greater rotational kinetic energy because $K_{\text{rot}}\propto I$ at fixed $\omega$ . (correct answer)
Their rotational kinetic energies depend only on $v$ of the center of mass.

Explanation: This question tests understanding of rotational kinetic energy. Rotational kinetic energy is calculated as K_rot = ½Iω², where I is the moment of inertia and ω is the angular speed. When two objects with equal mass rotate at the same angular speed ω but have different moments of inertia, the object with larger I has greater rotational kinetic energy. Since the first object has larger I than the second object, it has greater K_rot. Choice B incorrectly suggests that smaller I means larger energy at fixed ω, reversing the actual relationship. The key principle is that rotational kinetic energy is directly proportional to moment of inertia when angular speed is held constant.

Question 3

A wheel rotates about a fixed axle. Its angular speed increases, but the wheel's mass distribution about the axle is unchanged. Which quantity is sufficient to conclude that $K_{\text{rot}}$ increases?

Only the wheel's total mass increases.
Only the wheel's radius decreases.
Only the angular speed $\omega$ increases. (correct answer)
Only the linear speed of the axle increases.

Explanation: This question tests understanding of rotational kinetic energy. Rotational kinetic energy is K_rot = ½Iω², depending on moment of inertia I and angular speed ω squared. The problem states that mass distribution is unchanged, meaning I remains constant. If angular speed ω increases while I stays constant, then K_rot must increase due to the ω² dependence. Choice A (increasing mass) would change I, contradicting the given constraint, while choice D (linear speed of axle) is irrelevant to rotational kinetic energy about the axle. When a rigid body's angular speed increases with constant moment of inertia, its rotational kinetic energy must increase quadratically.

Question 4

A rigid rotor spins about a fixed axis. A student moves small masses outward along the rotor, increasing its moment of inertia, while keeping angular speed $\omega$ the same. What happens to rotational kinetic energy?

It decreases because the masses move farther from the axis.
It stays the same because $\omega$ is unchanged.
It increases because $K_{\text{rot}}=\tfrac12 I\omega^2$ and $I$ increases. (correct answer)
It becomes equal to the object's linear kinetic energy at the rim.

Explanation: This question tests understanding of rotational kinetic energy. Rotational kinetic energy is given by K_rot = ½Iω², where it depends linearly on moment of inertia I and quadratically on angular speed ω. When masses move outward along the rotor, they increase their distance from the axis, which increases the system's moment of inertia I. Since angular speed ω is kept constant, the rotational kinetic energy must increase proportionally with I. Choice B incorrectly assumes that constant ω means constant K_rot, ignoring the role of changing I. When analyzing rotational kinetic energy changes, consider both factors: changes in I (mass distribution) and changes in ω (rotation rate).

Question 5

A bicycle wheel rotates about its axle. The wheel is replaced by another wheel with the same mass and radius, but with more mass concentrated near the rim, and both spin with the same angular speed $\omega$ . Which wheel has greater rotational kinetic energy?

The replacement wheel, because concentrating mass farther from the axis increases $I$ and thus $K_{\text{rot}}$ . (correct answer)
The original wheel, because spreading mass inward increases rotational kinetic energy.
They have equal rotational kinetic energy because the masses and radii are the same.
They have equal rotational kinetic energy because the angular speeds are the same.

Explanation: This question assesses the concept of rotational kinetic energy in AP Physics 1. Rotational kinetic energy depends on moment of inertia I, which is larger when mass is concentrated farther from the axis of rotation. It also scales with the square of angular speed ω, but with ω constant, K_rot varies with I. Qualitatively, redistributing mass outward increases I and thus K_rot for the same ω, even if total mass and radius are unchanged. A common distractor is choice C, which assumes equal mass and radius imply equal I, ignoring mass distribution's effect on I. To evaluate rotational kinetic energy differences, consider how mass distribution affects I before applying the formula with given ω.

Question 6

A wheel rotates about its axle with angular speed $omega$ . The wheel is replaced by another with the same mass but a larger moment of inertia about the axle, while keeping $omega$ the same. Compared to before, $K_{rot}$ is:

smaller, because larger moment of inertia means less kinetic energy at the same angular speed.
the same, because the mass is the same.
larger, because $K_{rot}=\tfrac12 I\omega^2$ increases with $I$ when $omega$ is constant. (correct answer)
the same, because kinetic energy depends only on linear speed.

Explanation: This question tests understanding of rotational kinetic energy. Rotational kinetic energy is given by

K_{rot} = \frac{1}{2}I\omega^2

, where

I

is the moment of inertia and

\omega

is the angular speed. When the wheel is replaced with one having the same mass but larger moment of inertia, while keeping angular speed

\omega

constant, the rotational kinetic energy increases proportionally with

I

. This is because

K_{rot}

is directly proportional to

I

when

\omega

is held constant. Choice A incorrectly suggests an inverse relationship between moment of inertia and kinetic energy at constant angular speed. To analyze rotational kinetic energy changes, identify which variables (

I

\omega

) change and apply the formula

K_{rot} = \frac{1}{2}I\omega^2

directly.

Question 7

A uniform rod rotates about a fixed axis through its center, perpendicular to the rod. The rod's angular speed increases while its mass distribution stays unchanged. What happens to its rotational kinetic energy?

It increases, because rotational kinetic energy depends on $\omega$ (correct answer)
It decreases, because increasing rotation reduces translational motion
It stays the same, because the rod's mass is unchanged
It stays the same, because the axis is through the center

Explanation: This question tests understanding of rotational kinetic energy. Rotational kinetic energy is K_rot = ½Iω², depending on both moment of inertia I and angular speed ω squared. The rod's mass distribution (and thus I) stays unchanged, but ω increases. Since K_rot is proportional to ω², the rotational kinetic energy must increase. Choice C incorrectly assumes energy depends only on mass, not on how fast the object rotates. To analyze rotational energy changes, check whether I changes (mass distribution) and whether ω changes (rotation rate), then apply the formula.

Question 8

A uniform disk rotates about its central axis. It is replaced by a different object that has the same mass and angular speed $\omega$ but a larger moment of inertia about the same axis. The rotational kinetic energy of the new object is

greater (correct answer)
smaller
the same, because mass and $\omega$ are unchanged
the same, because rotational kinetic energy depends only on $\omega$

Explanation: This question tests understanding of rotational kinetic energy. Rotational kinetic energy is K_rot = ½Iω², depending directly on moment of inertia I when angular speed ω is constant. The new object has the same mass and ω but larger I than the original disk. Since K_rot is proportional to I (when ω is fixed), the new object must have greater rotational kinetic energy. Choice C incorrectly assumes mass alone determines energy, ignoring how that mass is distributed (which affects I). When comparing rotating objects, remember that same mass can yield different I values depending on mass distribution.

Question 9

Two rigid objects rotate about fixed axes through their centers. Object 1 has smaller $I$ but larger $\omega$ than Object 2. With no numbers given, which conclusion about their rotational kinetic energies is supported?

Object 1 definitely has greater rotational kinetic energy because it spins faster
Object 2 definitely has greater rotational kinetic energy because it has larger $I$
They must have equal rotational kinetic energy because both rotate about their centers
It cannot be determined without knowing both $I$ and $\omega$ (correct answer)

Explanation: This question tests understanding of rotational kinetic energy. Rotational kinetic energy is K_rot = ½Iω², depending on both moment of inertia I and angular speed ω squared. Object 1 has smaller I but larger ω, while Object 2 has larger I but smaller ω. Since K_rot depends on both I and ω², and these factors work in opposite directions for the two objects, we cannot determine which has greater energy without specific values. Choice A incorrectly assumes larger ω always means more energy, ignoring I. When comparing rotational energies without numbers, check if the competing factors (I and ω²) can be definitively ranked.

Question 10

Two objects rotate about the same fixed axis with the same angular speed $\omega$ . Object X has a larger moment of inertia about the axis than object Y. Which statement about rotational kinetic energy is correct?

Object Y has greater rotational kinetic energy because it is easier to spin
Object X has greater rotational kinetic energy because $K_\text{rot}=\tfrac12 I\omega^2$ (correct answer)
They have the same rotational kinetic energy because $\omega$ is the same
They have the same rotational kinetic energy because they rotate about the same axis

Explanation: This question tests understanding of rotational kinetic energy. Rotational kinetic energy is given by K_rot = ½Iω², showing it depends on both moment of inertia I and angular speed ω. Since both objects have the same ω but Object X has larger I, Object X has greater rotational kinetic energy. The formula directly shows that K_rot is proportional to I when ω is constant. Choice A incorrectly relates ease of spinning (which involves torque) to kinetic energy. To compare rotational kinetic energies, identify which quantities in K_rot = ½Iω² are the same and which differ.

Question 11

A rigid object rotates about a fixed axis with angular speed $\omega$ . The object is replaced by another with the same mass but smaller moment of inertia, while keeping $\omega$ the same. What happens to rotational kinetic energy?

It increases because smaller objects always have more kinetic energy.
It decreases because $K_{\text{rot}}=\tfrac12 I\omega^2$ and $I$ is smaller. (correct answer)
It stays the same because mass is the only factor affecting rotational kinetic energy.
It changes sign because the axis is fixed.

Explanation: This question tests understanding of rotational kinetic energy. Rotational kinetic energy is given by K_rot = ½Iω², showing direct proportionality to moment of inertia I when angular speed ω is constant. When the object is replaced by one with the same mass but smaller I (mass closer to the axis), while keeping ω unchanged, the rotational kinetic energy decreases proportionally with the decrease in I. Choice C incorrectly claims that only mass matters, ignoring how mass distribution (reflected in I) affects rotational kinetic energy. To analyze rotational kinetic energy changes, consider both factors separately: I (mass distribution relative to axis) and ω (rotation rate).

Question 12

Two objects rotate about the same fixed axis with the same angular speed $\omega$ . Object X has larger moment of inertia about that axis than object Y. Which is correct about their rotational kinetic energies?

Object Y has greater rotational kinetic energy because it is easier to spin.
They have equal rotational kinetic energy because $\omega$ is the same.
Object X has greater rotational kinetic energy because $K_{\text{rot}}\propto I$ for fixed $\omega$ . (correct answer)
Their rotational kinetic energies depend only on mass, not on $I$ .

Explanation: This question tests understanding of rotational kinetic energy. Rotational kinetic energy is given by K_rot = ½Iω², where I is the moment of inertia and ω is the angular speed. When two objects rotate at the same angular speed ω but have different moments of inertia, their kinetic energies differ proportionally to their I values. Since object X has larger I than object Y, and both have the same ω, object X has greater rotational kinetic energy. Choice A incorrectly suggests that smaller I (easier to spin) means greater energy, confusing ease of acceleration with energy content. The strategy is to recognize that at fixed angular speed, rotational kinetic energy is directly proportional to moment of inertia.

Question 13

A uniform rod rotates about an axis through its center, perpendicular to the rod. An identical rod rotates about a parallel axis through one end, with the same angular speed $\omega$ . Which has greater rotational kinetic energy?

The rod rotating about its center, because the center point has zero speed.
The rod rotating about one end, because its moment of inertia about that axis is larger. (correct answer)
They are equal because both rods have the same mass and length.
They are equal because rotational kinetic energy depends only on angular speed.

Explanation: This question tests understanding of rotational kinetic energy. Rotational kinetic energy depends on both moment of inertia and angular speed: K_rot = ½Iω². For a uniform rod of mass M and length L, the moment of inertia about the center is I_center = (1/12)ML², while about one end it is I_end = (1/3)ML². Since both rods rotate at the same angular speed ω, the rod rotating about its end has greater rotational kinetic energy because I_end = 4I_center. Choice A incorrectly focuses on the zero speed of the center point rather than the overall moment of inertia. To compare rotational kinetic energies, calculate or compare the moments of inertia about the given axes when angular speeds are equal.

Question 14

A solid disk rotates about its central axis. Without changing the disk, its angular speed is increased from $\omega$ to $2\omega$ . Which statement about the disk's rotational kinetic energy is correct?

It doubles because rotational kinetic energy depends linearly on $\omega$ .
It quadruples because $K_{\text{rot}}\propto \omega^2$ for fixed moment of inertia. (correct answer)
It is unchanged because the mass and radius of the disk are unchanged.
It becomes zero because the disk's center is not translating.

Explanation: This question tests understanding of rotational kinetic energy. Rotational kinetic energy is given by K_rot = ½Iω², where I is the moment of inertia and ω is the angular speed. Since the disk remains unchanged, its moment of inertia I stays constant. When angular speed doubles from ω to 2ω, the rotational kinetic energy becomes K_rot = ½I(2ω)² = ½I(4ω²) = 4(½Iω²), which is four times the original value. Choice A incorrectly assumes a linear relationship between K_rot and ω, when the relationship is actually quadratic. To solve rotational kinetic energy problems, identify what changes (ω, I, or both) and apply the quadratic dependence on ω and linear dependence on I.

Question 15

A rigid turntable rotates about a vertical axis through its center. At constant angular speed $\omega$ , a student compares two configurations: one with added masses near the center and one with the same masses near the edge. Which configuration has greater rotational kinetic energy?

Masses near the center, because smaller radius increases rotational kinetic energy.
Masses near the edge, because larger moment of inertia increases $K_{\text{rot}}$ at the same $\omega$ . (correct answer)
They are equal because the added masses are the same.
They are equal because the turntables angular speed is constant.

Explanation: This question assesses the concept of rotational kinetic energy in AP Physics 1. Rotational kinetic energy is influenced by moment of inertia I, which increases when added masses are placed farther from the axis due to the r² term in I. It depends on the square of angular speed ω, but with constant ω, differences stem from I. Qualitatively, masses at greater distances contribute more to I and thus to K_rot, enhancing energy storage. A common distractor is choice A, which wrongly claims smaller radius increases K_rot, reversing the actual effect of mass distribution on I. When adding masses to rotating systems, calculate or compare the resulting I values to predict changes in rotational kinetic energy.

Question 16

Two identical rigid disks rotate about the same fixed axis through their centers. Disk 1 rotates clockwise at angular speed $\omega$ , and Disk 2 rotates counterclockwise at the same $\omega$ . How do their rotational kinetic energies compare?

Disk 1 has greater rotational kinetic energy because clockwise rotation is positive.
Disk 2 has greater rotational kinetic energy because counterclockwise rotation is negative.
They are equal because rotational kinetic energy depends on $\omega^2$ , not direction. (correct answer)
They are not comparable without knowing their masses.

Explanation: This question assesses the concept of rotational kinetic energy in AP Physics 1. Rotational kinetic energy is proportional to moment of inertia I, which is identical for identical objects. It depends on the square of angular speed

\omega

, making it independent of rotation direction since

\omega^2

is always positive. Qualitatively, opposite directions do not affect the magnitude of K_rot, as energy is a scalar quantity. A common distractor is choice B, which mistakenly treats rotational kinetic energy as direction-dependent, like angular velocity, but energy uses

\omega^2

. For problems involving direction, remember that rotational kinetic energy uses

\omega^2

, eliminating directional effects in comparisons.

Question 17

Object 1 definitely has greater rotational kinetic energy because it spins faster
Object 2 definitely has greater rotational kinetic energy because it has larger $I$
They must have equal rotational kinetic energy because both rotate about their centers
It cannot be determined without knowing both $I$ and $\omega$ (correct answer)

Explanation: This question tests understanding of rotational kinetic energy. Rotational kinetic energy is K_rot = ½Iω², depending on both moment of inertia I and angular speed ω squared. Object 1 has smaller I but larger ω, while Object 2 has larger I but smaller ω. Since K_rot depends on both I and ω², and these factors work in opposite directions for the two objects, we cannot determine which has greater energy without specific values. Choice A incorrectly assumes larger ω always means more energy, ignoring I. When comparing rotational energies without numbers, check if the competing factors (I and ω²) can be definitively ranked.

Question 18

Object Y has greater rotational kinetic energy because it is easier to spin
Object X has greater rotational kinetic energy because $K_\text{rot}=\tfrac{1}{2} I \omega^2$ (correct answer)
They have the same rotational kinetic energy because $\omega$ is the same
They have the same rotational kinetic energy because they rotate about the same axis

Explanation: This question tests understanding of rotational kinetic energy. Rotational kinetic energy is given by

K_\text{rot} = \frac{1}{2} I \omega^2

, showing it depends on both moment of inertia I and angular speed

\omega

. Since both objects have the same

\omega

but Object X has larger I, Object X has greater rotational kinetic energy. The formula directly shows that

K_\text{rot}

is proportional to I when

\omega

is constant. Choice A incorrectly relates ease of spinning (which involves torque) to kinetic energy. To compare rotational kinetic energies, identify which quantities in

K_\text{rot} = \frac{1}{2} I \omega^2

are the same and which differ.

Question 19

It increases, because rotational kinetic energy depends on $\omega$ (correct answer)
It decreases, because increasing rotation reduces translational motion
It stays the same, because the rod's mass is unchanged
It stays the same, because the axis is through the center

Question 20

A fan rotates about a fixed axle. Its angular speed stays constant, but several small pieces of tape are added near the blade tips, increasing the fan's moment of inertia. What happens to $K_{\text{rot}}$ ?

It increases because $I$ increases while $\omega$ is unchanged. (correct answer)
It decreases because added mass slows the fan's rotation automatically.
It is unchanged because rotational kinetic energy depends only on $\omega$ .
It is unchanged because tape adds negligible linear kinetic energy.

Explanation: This question assesses understanding of rotational kinetic energy. Rotational kinetic energy is expressed as ( K_{

\text{rot}

} =

\frac{1}{2}

\omega^2

), depending on moment of inertia ( I ), which increases with mass added farther from the axis, and on (

\omega^2

). Adding tape near the blade tips raises ( I ) because it contributes more to the (

mr^2

) terms in ( I ). With (

\omega

) held constant, the energy increases linearly with the rise in ( I ). A distractor like choice C erroneously claims the energy depends only on (

\omega

), disregarding the role of ( I ). For related problems, evaluate how modifications affect ( I ) and then apply the energy formula, assuming constants as stated.