Examples of Rotational Systems (College Board AP® Physics 1: Algebra-Based): Exam Questions

Two planets, X and Y, have the same mass. Planet X has a greater surface gravity than Planet Y.

Which planet has a greater escape velocity?

A bowling ball of mass $5.0\mathrm{kg}$ and radius $12.0\mathrm{cm}$ rolls along a horizontal surface with a velocity of $8\mathrm{m}/\mathrm{s}$. The ball is a solid sphere with a rotational inertia of $I=\frac{2}{5}m{r}^2$.

Which of the following is most nearly the total kinetic energy of the bowling ball?

A hollow cylinder and a solid cylinder of the same mass and radius are released from rest at the top of an inclined ramp. Both roll down the ramp without slipping.

Which cylinder reaches the bottom of the ramp first, and why?

Two satellites, X and Y, of equal mass, orbit a planet at radii $R$ and $2R$ respectively.

Which one of the following statements is true about the kinetic and potential energies of the satellites?

A soccer ball of mass $m$ and radius $r$ rolls along a horizontal surface without slipping. The soccer ball can be modeled as a hollow sphere of rotational inertia $\frac{2}{3}m{r}^2$.

Which of the following is most nearly the proportion the rotational kinetic energy contributes to the total kinetic energy of the soccer ball?

A solid ball of mass $M$ and radius $R$ has rotational inertia $\frac{2}{5}M{R}^2$ about its center. It rolls without slipping along a level surface at speed $v$ just before it begins rolling up an inclined plane.

Which of the following expressions correctly represents the maximum vertical height the solid ball can ascend to when it rolls up the incline without slipping?

A probe is launched vertically upwards from the Earth's surface with a velocity equal to half the required escape velocity from this point.

If the radius of the Earth is $R$, which of the following expressions correctly describes the maximum height reached by the probe?

A satellite of mass $m$ is initially in a circular orbit of radius $r_1$ around the Earth, which has a radius of $R$ and surface gravity $g$.

Which of the following correctly describes the work done by gravity when a satellite is moved from its initial orbital radius $r_1$ to a larger orbital radius $r_2$?

In Experiment 1, a solid disk of rotational inertia $\frac{1}{2}m{r}^2$ is released from rest at the top of a ramp where the frictional force is such that the disk rolls without slipping. In Experiment 2, the same disk is released from rest at the top of an identically shaped ramp where the frictional force is such that the disk rolls and slips. The energy bar chart in the figure represents the gravitational potential energy $U_g$ of the disk-Earth systems, and the translational kinetic energy $K_t$ and rotational kinetic energy $K_r$ of the disks just before their release.

Which of the following graphs could represent the energy bar charts for the disks at the bottom of the ramps in each experiment?

In an experiment, a solid sphere is released from the top of three tracks which are identical in size and shape, but have different coefficients of friction. In each trial, the sphere is released from rest at the same point and leaves the track at point X, as shown in the figure. In Trial 1, the sphere rolls without slipping along the entire track. In Trial 2, the sphere rolls and slips down the first slope and rolls without slipping up the next slope. In Trial 3, the sphere moves along a track with negligible friction. The maximum heights reached by each sphere after leaving the track are $h_1$, $h_2$, and $h_3$ respectively.

Which of the following correctly ranks $h_1$, $h_2$, and $h_3$ from greatest to least?