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

A winch used to lift heavy crates consists of a cable wound around a drum of diameter $2.5\mathrm{m}$, as shown in the figure. The maximum torque the winch can withstand without breaking is $1250\mathrm{N}·\mathrm{m}$.

Which of the following most nearly represents the maximum mass of the crate the winch could lift without breaking?

Forces are exerted on four identical rods, as shown in the figure.

Which of the following correctly ranks the magnitude of the net torque about the pivot on the left end of each rod from greatest to least?

A uniform rigid bar of weight $W$ is pivoted at point O and is supported by a rope that makes a 30° angle with the horizontal axis, as shown in the figure.

Which of the following diagrams best represents the directions of the forces acting on the bar?

Two forces $F_1$ and $F_2$ act on a gate of length $L$ and produce torques of magnitude ${\tau }_1$ and ${\tau }_2$ respectively. Force $F_1$ acts at the midpoint of the gate, perpendicular to its surface. Force $F_2$ acts at the free end of the gate, at an angle of 30° to its surface.

How does ${\tau }_1$ compare to ${\tau }_2$?

Two flywheels, of radii $2R$ and $3R$ respectively, are joined together and free to rotate about a common axis through their centers. Forces $F_1$ and $F_2$ are applied to light cords which are wound around the larger and smaller flywheels respectively, as shown in the figure.

If the magnitudes of the torques produced are equal, which of the following statements correctly describes the magnitudes of $F_1$ and $F_2$?

A pendulum of length $L$ with a bob of mass $m$ is suspended from point P, as shown in the figure.

Which of the following expressions correctly represents the torque exerted on the pendulum about point P when released from an angle of 60° below the horizontal?

A door handle of length $10\mathrm{cm}$ requires a force of at least $20\mathrm{N}$ to turn it about an axle of diameter $0.5\mathrm{cm}$, as shown in the figure. One day, the handle breaks and the door can only be opened using the axle of the handle.

Which of the following is most nearly the force required to open the door when the handle is broken?

A light uniform rod made up of two segments, AB and BC, of lengths $50\mathrm{cm}$ and $40\mathrm{cm}$ respectively, is attached to the wall at point A, as shown in the figure. Rod BC makes an angle of $60°$ with rod AB. A force of $20\mathrm{N}$ is exerted horizontally at point C on the rod.

Which of the following is most nearly the magnitude of the torque produced by the $20\mathrm{N}$ force about point A?

Four forces are applied to a wheel which is free to rotate about its central axis through point O, as shown in the figure. Forces $F_1=6.0\mathrm{N}$, $F_2=4.0\mathrm{N}$, and $F_4=8.0\mathrm{N}$ are applied at the radius $R$ of the wheel. Force $F_3=4.0\mathrm{N}$ is applied at a distance $r$, which is the midpoint between point O and the edge of the wheel.

Which of the following correctly ranks the magnitude of the torques produced by their corresponding forces about the rotation axis at point O from greatest to least?

A uniform ladder of mass $m$ leans against a wall while a person of mass $M$ stands on it, as shown in the figure. The ladder does not slip. The coefficient of the static friction between the ladder and the wall is $\frac{1}{3}$ and the coefficient of the static friction between the ladder and the ground is $\frac{2}{5}$.

Which of the following best represents the forces acting on the ladder and the number of torques applied about the base of the ladder?

	Force Diagram	Number of Torques
‎ ‎ ‎ ‎‎‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ A‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎		‎ ‎ ‎ ‎ ‎ ‎ ‎‎ ‎ 4 ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎
‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ B‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎		‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ 2‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎
‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ C‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎		‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ 4‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎
‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ D‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎		‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ 2‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎