Study GuidesExam QuestionsPast Papers
AP®PhysicsCollege BoardPhysics 1: Algebra-BasedExam QuestionsUnit 5: Torque & Rotational DynamicsRotational Inertia

Rotational Inertia (College Board AP® Physics 1: Algebra-Based): Exam Questions

15 mins15 questions

Select a download format for Rotational Inertia

Scroll for more
Easy
Medium
Hard
1
Sme Calculator1 mark

Which of the following statements is true about the rotational inertia of a rigid system?

  • Rotational inertia depends only on the total mass of the system.

  • Rotational inertia depends on the total mass of the system and the distribution of mass relative to an axis of rotation.

  • Rotational inertia is the same for all rigid systems with the same mass.

  • Rotational inertia does not depend on the shape of the rigid system.

Choose your answer

Did this page help you?

2
Sme Calculator1 mark

Object

Mass (kg)

Distance from axis (m)

1

2.0

1.0

2

1.5

0.5

3

3.0

1.5

The masses of three objects and their distances relative to a rotational axis are listed in the table above.

Which of the following is most nearly the total rotational inertia of the system?

  • 7 space kg times straight m squared

  • 9 space kg times straight m squared

  • 19 space kg times straight m squared

  • 25 space kg times straight m squared

Choose your answer

Did this page help you?

3
Sme Calculator1 mark

A thin ring of mass m and radius r attached to a solid disc of mass 2 m and radius r rotates about an axis passing through both their centers. The rotational inertia of a thin ring about its center is M R squared, and 1 half M R squared for a solid disc.

Which of the following expressions correctly represents the total rotational inertia of the ring and disc?

  • 1 half m r squared

  • m r squared

  • 3 over 2 m r squared

  • 2 m r squared

Choose your answer

Did this page help you?

4
Sme Calculator1 mark
A grey cylinder with a dashed diagonal axis, showing a 4 cm distance marked from the axis to a point on the front circular face.

A uniform cylinder with a radius of 8.0 cm and a mass of 5 kg has a rotational inertia of 0.016 kg⋅m2 about its central axis. The cylinder is mounted to an axis parallel to, and 4.0 cm from, the central axis of the cylinder, as shown in the figure.

Which of the following is most nearly the rotational inertia of the cylinder about the axis of rotation?

  • 0.008 space kg times straight m squared

  • 0.012 space kg times straight m squared

  • 0.024 space kg times straight m squared

  • 0.048 space kg times straight m squared

Choose your answer

Did this page help you?

5
Sme Calculator1 mark
Two diagrams labeled "Experiment 1" and "Experiment 2" show rotating discs with arrows indicating rotation. Both have radius markers labeled "r."

In Experiment 1, a solid disk of mass m and radius r is made to rotate about an axis passing through its center and is found to have a rotational inertia of 1 half m r squared about this axis. In Experiment 2, the same disk is made to rotate about an axis through the edge of the disk, as shown in the figure.

Which of the following expressions correctly describes the rotational inertia of the disk in Experiment 2?

  • 1 half m r squared

  • m r squared

  • 3 over 2 m r squared

  • 2 m r squared

Choose your answer

Did this page help you?

1
Sme Calculator1 mark
Four particles arranged at the corners of a square with an axis of rotation shown as a dashed line. Labels "L" mark two sides.

Four objects, each of mass M, are placed at the corners of a square with side length L and arranged such that the axis of rotation lies in the plane of the objects, as shown in the figure.

Which of the following expressions correctly represents the rotational inertia of this configuration?

  • 1 half M L squared

  • M L squared

  • 2 M L squared

  • 4 M L squared

Choose your answer

Did this page help you?

2
Sme Calculator1 mark
Diagram showing a solid disk and a hoop, each with radius R and mass M, attached to a vertical rod under a horizontal platform.

Two pulleys of equal mass and radius are mounted on a frictionless horizontal axis through their centers, as shown in the figure. One pulley is a uniform solid disk, and the other is a hoop.

How does the rotational inertia of each pulley compare, and why?

  • The pulleys have the same rotational inertia because they have the same mass and radius.

  • The solid disk pulley has a greater rotational inertia because its mass is evenly distributed.

  • The hoop pulley has a greater rotational inertia because its mass is distributed further from its center.

  • The pulleys have different rotational inertia, but not enough information is provided to determine which is greater.

Choose your answer

Did this page help you?

3
Sme Calculator1 mark
A rod of length L with its length along the x-axis and the y-axis through its center. Two dashed lines parallel to the y-axis indicate lines passing through points x = -L/2 and x = L/4.

A thin uniform rod of length L lies along the x-axis, as shown in the figure.

Which of the following correctly describes the axes about which the rod has the smallest and greatest rotational inertia?

Smallest Rotational Inertia

Greatest Rotational Inertia

A

x-axis

line x space equals space minus L over 2

B

y-axis

line x space equals space minus L over 2

C

x-axis

line x space equals space L over 4

D

y-axis

line x space equals space L over 4

    Choose your answer

    Did this page help you?

    4
    Sme Calculator    1 mark
    Diagram of a rectangle with circles at corners, labelled sides 'a' and 'b'. An angled arrow originates from one side, indicating the rotational axis.

    Four objects, each of mass m, are arranged at the corners of a rectangle that rotates about an axis perpendicular to the midpoint of one of the sides of the rectangle and out of the page, as shown in the figure.

    Which of the following expressions correctly represents the total rotational inertia of the system?

    • fraction numerator m a squared over denominator 2 end fraction

    • m open parentheses a squared over 2 space plus space 2 b squared close parentheses

    • m open parentheses 2 a squared space plus space b squared close parentheses

    • m open parentheses a squared space plus space 2 b squared close parentheses

    Choose your answer

    Did this page help you?

    5
    Sme Calculator    1 mark

    Two objects are connected by a massless rod to form a dumbbell.

    Which of the following diagrams shows the dumbbell with the greatest rotational inertia about an axis perpendicular to the rod and passing through its center?

    • Two black circles labelled "2m" connected by a horizontal line labelled "L," representing a diagram of a physical system or model.
    • Diagram showing two masses, labelled 'm', connected by a line of length '2L'. The masses are represented as black dots at each end.
    • Two connected circles, labelled 'm' and '2m', with a rod of length 'L' joining them, representing a simple physical model.
    • Two black circles connected by a line. The left circle is labelled 2m, the right circle is m, and the line between is labelled 2L.

    Choose your answer

    Did this page help you?

    1
    Sme Calculator    1 mark
    Diagram of a mechanical system showing a block connected to a rod, which pivots on a disk labeled "R." The setup is mounted on a horizontal base.

    A uniform disk of mass M and radius R is mounted to a frictionless axle, as shown in the figure. A thin uniform rod of mass 1 fourth M and length 2 R is rigidly attached to the disk so that they rotate together. A block of mass 2 over 3 M is attached to the end of the rod.

    The rotational inertia of the disk about its center is 1 half M R squared. The rotational inertia of a rod about one end is 1 third m L squared, where m is the mass of the rod and L is the length.

    Which of the following expressions correctly represents the total rotational inertia of the disk, rod, and block?

    • 1 half M R squared

    • 2 M R squared

    • 5 over 2 M R squared

    • 7 over 2 M R squared

    Choose your answer

    Did this page help you?

    21 mark
    Two spheres, labeled 3M and M, connected by a massless rod. Vertical lines represent axes A, B, C, D at distances from the 3M mass of 0, L/4, L/2, and L respectively.

    Two solid spheres of unequal mass and radius are connected by a massless rod of length L. The rotation of the two-sphere system is considered about four parallel axes, A, B, C, and D, as shown in the figure. The sphere on axis A has mass 3 M, and the sphere on axis D has mass M. The rotational inertias of the two-sphere system about the axes are I subscript A, I subscript B, I subscript C, and I subscript D, respectively.

    Which of the following correctly ranks I subscript A, I subscript B, I subscript C, and I subscript D from greatest to least?

    • I subscript D space greater than space I subscript C space greater than space I subscript A space greater than space I subscript B

    • I subscript B space greater than space I subscript C space greater than space I subscript A space greater than space I subscript D

    • I subscript B space greater than space I subscript C space equals space I subscript A space greater than space I subscript D

    • I subscript D space greater than space I subscript C space equals space I subscript A space greater than space I subscript B

    Choose your answer

    Did this page help you?

    3
    Sme Calculator    1 mark
    Two hemispheres on opposite sides of a horizontal line, with dotted vertical line AB representing the rotational axis.

    Two identical solid hemispheres, each of mass m and radius r are joined together and allowed to rotate about axis AB, as shown in the figure. The rotational inertia of a solid sphere of mass M and radius R about its center is 2 over 5 M R squared.

    Which of the following expressions correctly represents the rotational inertia of this system about axis AB?

    • 6 over 5 m r squared

    • 7 over 5 m r squared

    • 12 over 5 m r squared

    • 14 over 5 m r squared

    Choose your answer

    Did this page help you?

    4
    Sme Calculator    1 mark

    A thin circular disc of mass M and radius R has rotational inertia I space equals space 1 half M R squared about an axis passing through its center and perpendicular to its plane. The same disc has rotational inertia I over 2 about an axis passing through its center and parallel to its plane.

    Which of the following expressions gives the rotational inertia of the disc about an axis tangential to its edge and parallel to its plane?

    • fraction numerator 2 I over denominator 5 end fraction

    • fraction numerator 2 I over denominator 3 end fraction

    • fraction numerator 3 I over denominator 2 end fraction

    • fraction numerator 5 I over denominator 2 end fraction

    Choose your answer

    Did this page help you?

    5
    Sme Calculator    1 mark
    Diagram of two identical spheres, labelled M, R, connected by a rod marked 6R. An axis is shown vertically at the rod's midpoint.

    Two uniform solid spheres of mass M and radius R are connected by a cylindrical rod of mass 1 half M, length 6 R, and radius 1 fifth R. The system is made to rotate about an axis through the system's center of mass, as shown in the figure. The rotational inertia of a solid sphere about its center is 2 over 5 M R squared. The rotational inertia of a cylinder of length L about a central axis perpendicular to its length is 1 fourth M R squared space plus thin space 1 over 12 M L squared.

    Which of the following is most nearly the proportion the cylindrical rod contributes to the total rotational inertia of the system about its center of mass?

    • 4 percent sign

    • 7 percent sign

    • 11 percent sign

    • 32 percent sign

    Choose your answer

    Did this page help you?