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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

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1
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Which of the following correctly describes the condition for a system to be in rotational equilibrium?

  • sum F space equals space 0

  • sum tau space equals space 0

  • sum F space equals space 0 and sum tau space equals space 0

  • sum F space not equal to space 0 and sum tau space not equal to space 0

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2
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A wheel with a force F0 applied downwards to a point on its rim directly to the left of its center.

A wheel initially rotates about its center with a constant angular speed in the clockwise direction. A constant force F subscript 0 is exerted on the wheel, as shown in the figure.

Which of the following correctly describes the angular acceleration of the wheel at the moment the force is applied?

  • The angular acceleration is zero.

  • The angular acceleration is in the clockwise direction.

  • The angular acceleration is in the counterclockwise direction.

  • The direction of the angular acceleration cannot be determined.

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3
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A rigid body with constant rotational inertia experiences a net torque.

Which of the following correctly describes the relationship between the net torque and the angular acceleration of the rigid body?

  • A larger net torque results in a larger angular acceleration.

  • A larger net torque results in a smaller angular acceleration.

  • Angular acceleration is independent of torque.

  • Torque only affects angular velocity, not angular acceleration.

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4
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Two blocks of masses M and 2 M are placed on a seesaw at different distances from the central fulcrum.

Which of the following diagrams could represent an arrangement of blocks that would balance the seesaw?

  • Seesaw with the block of mass M stacked on top of the block of mass 2M. The blocks are positioned about halfway between the fulcrum and the left end of the seesaw.
  • Seesaw with the block of mass 2M positioned at the left end and the block of mass M positioned at the right end.
  • Seesaw with the block of mass 2M positioned at the left end and the block of mass M positioned about halfway between the fulcrum and the right end.
  • Seesaw with the block of mass 2M positioned about halfway between the fulcrum and the left end and the block of mass M positioned at the right end.

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5
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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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1
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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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2
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Two wheels 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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3
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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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4
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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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5
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An object of mass m is placed at the 20 cm mark on a uniform meterstick of mass 1.5 m.

If an object of mass 2 mis placed at the 90 cm mark, which of the following points on the meterstick should the fulcrum be placed to balance the system?

  • At the 40 cm mark.

  • At the 45 cm mark.

  • At the 55 cm mark.

  • At the 60 cm mark.

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1
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Block A connected to block B by a string which passes over a pulley of radius R. Block A is suspended from the pulley, while block B rests on a horizontal surface.

Blocks A and B, of masses m subscript A and m subscript B, respectively, are joined by a light string that passes over a pulley, as shown in the figure. The pulley has a radius R and a rotational inertia 1 half M R squared about its center. The string does not slip on the pulley as block B accelerates along the horizontal frictionless surface and block A accelerates vertically downwards.

Which of the following gives the magnitude of the linear acceleration of the blocks?

  • fraction numerator open parentheses m subscript A space minus space m subscript B close parentheses g over denominator m subscript A space plus space m subscript B end fraction

  • fraction numerator m subscript A g over denominator m subscript A space plus space m subscript B space plus thin space M end fraction

  • fraction numerator m subscript A g over denominator m subscript A space plus space m subscript B space plus thin space M over 2 end fraction

  • fraction numerator m subscript A g R over denominator m subscript A space plus space m subscript B space plus thin space M over 2 end fraction

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2
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A rod of length L pivoted at its left end and a string attached vertically to its right end keeps it horizontally aligned. A sphere of radius R is attached at the other end at the rod.

A hollow sphere of mass 1 space kg and radius R space equals space 0.5 space straight m is attached to the end of a thin uniform rod of mass 3 space kg and length L space equals space 1.5 space straight m. The rod is free to rotate about a pivot at its left end and held horizontally by a string at its right end, as shown in the figure. With respect to the pivot, the rod has rotational inertia 1 third M L squared. The rotational inertia of a hollow sphere about its center is 2 over 3 M R squared.

If the string breaks, which of the following is most nearly the angular acceleration of the rod immediately after the system is released?

  • 6 space rad divided by straight s squared

  • 7 space rad divided by straight s squared

  • 16 space rad divided by straight s squared

  • 18 space rad divided by straight s squared

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3
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A thin rod with object A on the left end, object B on the right end, and an off-center pivot. The distance from object A to the pivot is L, and the distance from object B to the pivot is 2L.

Objects A and B, of masses M subscript A and M subscript B respectively, are attached to a light rigid rod, as shown in the figure. When the system is released from rest, it begins to rotate counterclockwise about the pivot with angular acceleration fraction numerator g over denominator 7 L end fraction.

Which of the following expressions correctly represents the mass of object A?

  • 1 half M subscript B

  • 5 over 4 M subscript B

  • 3 M subscript B

  • 17 M subscript B

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4
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Diagram of a ladder of length L leaning against a wall, forming an angle θ with the wall.

A thin uniform ladder of length L rests against a frictionless wall at an angle theta, as shown in the figure. The coefficient of friction between the ladder and the ground is mu.

Which of the following expressions gives the minimum value of mu required to stop the ladder from sliding?

  • fraction numerator tan space theta over denominator 2 end fraction

  • 1 half

  • fraction numerator 1 over denominator 2 space tan space theta end fraction

  • 2 space tan space theta

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5
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Diagram of a block on an inclined plane with angle θ, connected via pulley to another block. Pulley radii are r and 2r; blocks are labeled m1 and m2.

Two masses, m subscript 1 and m subscript 2, are attached to light strings which are wound around two frictionless pulleys of radii r and 2 r respectively, which are free to rotate about the same axle at their centers, as shown in the figure. When mass m subscript 1 is placed on a frictionless ramp that makes an angle theta with the horizontal and mass m subscript 2 is suspended from the pulley, the system is in static equilibrium.

Which of the following expressions correctly relates the sizes of the two masses?

  • m subscript 2 space equals space fraction numerator m subscript 1 over denominator 2 space sin space theta end fraction

  • m subscript 2 space equals space fraction numerator m subscript 1 space sin space theta over denominator 2 end fraction

  • m subscript 2 space equals space fraction numerator 2 m subscript 1 over denominator sin space theta end fraction

  • m subscript 2 space equals space 2 m subscript 1 space sin space theta

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