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AP®PhysicsCollege BoardPhysics 1: Algebra-BasedExam QuestionsUnit 5: Torque & Rotational DynamicsNewton’s First & Second Law in Rotational Form

Newton’s First & Second Law in Rotational Form (College Board AP® Physics 1: Algebra-Based)

Exam Questions

5 mins5 questions
1
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Diagram of a pulley system with two masses (m1 and m2). Radii r1 and r2 are indicated, where m2 is attached to a smaller radius pulley, and m1 to a larger radius pulley.

Two masses, m subscript 1 and m subscript 2, are attached to light cords which are wrapped around axles at distances r subscript 1 and r subscript 2 from the center of a pulley respectively, as shown in the figure.

Which of the following expressions is true if the system is in rotational equilibrium?

  • m subscript 1 space equals space m subscript 2

  • m subscript 1 r subscript 1 space equals space m subscript 2 r subscript 2

  • m subscript 1 r subscript 2 space equals space m subscript 2 r subscript 1

  • m subscript 1 r subscript 1 superscript 2 space equals space m subscript 2 r subscript 2 superscript 2

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2
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Diagram showing a pulley system with two masses. Mass m1 is suspended higher than mass m2, with height h between them. Pulley has radius R and mass M.

Two masses, m subscript 1 space equals space 5.0 space kg and m subscript 2 space equals space 3.0 space kg, are suspended by a rope that goes over a pulley of radius R space equals space 0.2 space straight m and mass M space equals space 10 space kg, as shown in the figure. The rotational inertia of the pulley is I space equals space 1 half M R squared. The pulley can rotate about its center with negligible friction. Initially, mass m subscript 2 is on the ground, and mass m subscript 1 is suspended at a height habove the ground.

When the masses are released, which of the following is most nearly the angular acceleration of the pulley?

  • 4 space rad divided by straight s squared

  • 10 space rad divided by straight s squared

  • 20 space rad divided by straight s squared

  • 40 space rad divided by straight s squared

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3
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Diagram showing two concentric circles with radii 2R and 3R, and forces labeled F and 2F acting in horizontal and vertical directions.

A system of two wheels, of radii 2 R and 3 R respectively, are joined together and free to rotate about a frictionless axis through their common center. Four forces are exerted tangentially to the rims of the wheels, as shown in the figure.

Which of the following correctly represents the magnitude of the net torque on the system about the axis?

  • 2 F R

  • 4 F R

  • 8 F R

  • 16 F R

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4
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Diagram of a wheel with initial angular velocity ω₀. Two forces F and 2F are applied downward on the left and right sides, respectively.

A disk is initially rotating counterclockwise around a fixed axis with angular speed omega subscript 0. At time t = 0, two forces are exerted on the disk as shown in the figure.

Taking counterclockwise as the positive direction, which of the following is the best representation of the angular velocity of the disk as a function of time?

  • Graph with time (t) on the horizontal axis and frequency (ω) on the vertical axis, showing a straight line starting from the origin.
  • Graph with horizontal axis labeled 't' and vertical axis labeled 'ω'. Points O and -ω0 are marked on the axes.
  • Graph of angular velocity (ω) versus time (t) showing a linear decrease from initial angular velocity (ω₀) at t=0, intersecting the time axis at a positive value.
  • Graph showing angular velocity (ω) on the vertical axis and time (t) on the horizontal axis. The plot starts at ω0, drops to zero, and then linearly increases.

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5
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Diagram of a rod attached to a vertical pivot, forming a 60-degree angle. The rod rotates around the pivot point on a vertical surface.

A uniform rod of mass M and length L is free to rotate about a pivot at its left end and is released from rest when the rod is 60° above the horizontal, as shown in the figure. The angular acceleration of the rod is alpha subscript 0at the moment it is released.

Which of the following expressions correctly represents the magnitude of the angular acceleration of the rod at the moment it passes through the horizontal position?

  • 1 half alpha subscript 0

  • alpha subscript 0

  • 2 alpha subscript 0

  • The answer cannot be determined without knowing the rod's rotational inertia.

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