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

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

Exam Questions

5 mins5 questions
1
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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

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2
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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 its center of mass 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

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3
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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.

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4
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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

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51 mark
Diagram with two circles connected by a line, labeled 3M and M. Vertical lines labeled A, B, C, D indicate distances L/4, L/2, and L.

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

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