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AP®PhysicsCollege BoardPhysics 1: Algebra-BasedExam QuestionsUnit 6: Energy & Momentum of Rotating SystemsAngular Momentum & Angular Impulse

Angular Momentum & Angular Impulse (College Board AP® Physics 1: Algebra-Based)

Exam Questions

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1
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Diagram depicting two figures at the ends of a 12-meter rod, rotating around its center marked CM, with arrows indicating rotational direction.

Two astronauts each of mass 70 kg are connected by a 12 m rope of negligible mass. They are isolated in space, orbiting their center of mass at a speed of 4.0 m/s, as shown in the figure.

Which of the following is most nearly the magnitude of the angular momentum of the system?

  • 0

  • 1700 space kg times straight m squared divided by straight s

  • 3400 space kg times straight m squared divided by straight s

  • 6800 space kg times straight m squared divided by straight s

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2
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Diagram showing two green rectangular beams, labeled X and Y, rotating around vertical axes. The beam X has an inertia of 1/12 ML^2, and Y has 1/3 ML^2.

Two identical rods, X and Y, each of length L and mass M, are each made to rotate about different vertical axes, so they have different values of rotational inertia, as shown in the figure.

Which of the following expressions correctly relates the angular speeds of X and Y if they have equal angular momenta?

  • omega subscript straight X space equals space 1 fourth omega subscript straight Y

  • omega subscript straight X space equals space 1 half omega subscript straight Y

  • omega subscript straight X space equals space 2 omega subscript straight Y

  • omega subscript straight X space equals space 4 omega subscript straight Y

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3
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Diagram of a rotating system with four masses connected by rods. Two arms of length L with mass m at ends, and two perpendicular arms of length 2L with mass 2m at ends.

A rigid body consists of a vertical support post and two horizontal rods of negligible mass. Masses are attached to the ends of the horizontal rods, as shown in the figure. The body rotates about a vertical axis along the support post with constant angular speed omega.

What is the ratio of the angular momentum of the two upper spheres to that of the two lower spheres?

  • 1 over 8

  • 1 fourth

  • 1 half

  • 2

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4
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A constant force of 250 space straight N is applied tangentially to the outer edge of a playground merry-go-round of radius 2.0 space straight m to rotate it from rest. A frictional force of 50 space straight N is exerted tangentially at a distance of 25 space cm from the axis of rotation. The rotational inertia of the merry-go-round is 1500 space kg times straight m squared.

Which of the following is most nearly the angular speed of the merry-go-round if the force is applied for 5 seconds?

  • 0.17 space rad divided by straight s

  • 0.33 space rad divided by straight s

  • 1.3 space rad divided by straight s

  • 1.6 space rad divided by straight s

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5
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Graph showing torque (τ) in Newton-meters (N·m) versus time (t) in seconds (s). The torque rises linearly to 3 N·m from 0 to 2s, stays constant until 4s, then drops linearly to 0 by 5s.

A disk with a rotational inertia of 0.11 kg∙m2 is mounted on a frictionless horizontal axle. The graph shows the torque applied to the outer rim of the disk as a function of time.

If the disk is initially at rest, what is the minimum time it takes for the disk to spin at a rate of 10 revolutions per second?

  • t space equals space 2 space straight s

  • t space equals space 3 space straight s

  • t space equals space 4 space straight s

  • t space equals space 5 space straight s

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