AP-Style Practice QuestionsAP 风格练习题
Topics主题 6.1 - 6.6MECH
Show all supporting work on scratch paper. Each item is labeled with its Mechanics topic and whether a calculator is permitted on that AP Exam section. Take $g = 9.8~\mathrm{m/s^2}$ unless a problem says otherwise; $G = 6.67 \times 10^{-11}~\mathrm{N \cdot m^2/kg^2}$.请在草稿纸上写出所有辅助计算过程。每道题均标注了对应的力学主题以及该 AP 考试部分是否允许使用计算器。除非题目另有说明，取 $g = 9.8~\mathrm{m/s^2}$；$G = 6.67 \times 10^{-11}~\mathrm{N \cdot m^2/kg^2}$。
A flywheel of moment of inertia $I = 2.0~\mathrm{kg \cdot m^2}$ spins about its axis at $\omega = 3.0~\mathrm{rad/s}$. Its rotational kinetic energy is一个转动惯量为 $I = 2.0~\mathrm{kg \cdot m^2}$ 的飞轮以 $\omega = 3.0~\mathrm{rad/s}$ 绕轴旋转。其转动动能为
A particle of mass $2.0~\mathrm{kg}$ moves at $3.0~\mathrm{m/s}$ in a circle of radius $0.50~\mathrm{m}$. The magnitude of its angular momentum about the center of the circle is一个质量为 $2.0~\mathrm{kg}$ 的质点以 $3.0~\mathrm{m/s}$ 的速度在半径 $0.50~\mathrm{m}$ 的圆形轨道上运动。其相对于圆心的角动量大小为
A spinning ice skater pulls her arms in toward her body. With no external torques acting on her, her angular speed一位旋转的花样滑冰运动员将手臂向身体收拢。在没有外力矩作用的情况下，她的角速度
A satellite is in a circular orbit around Earth. As the orbital radius is increased, the satellite's orbital speed一颗卫星围绕地球做圆轨道运动。随着轨道半径增大，卫星的轨道速度
A solid disk and a thin hoop have the same mass $M$ and the same radius $R$, and rotate about their central axes at the same angular speed $\omega$. The ratio of the disk's rotational kinetic energy to the hoop's rotational kinetic energy is一个实心圆盘和一个细圆环质量均为 $M$，半径均为 $R$，以相同的角速度 $\omega$ 绕各自的中心轴旋转。圆盘的转动动能与圆环的转动动能之比为
A constant torque of $5.0~\mathrm{N \cdot m}$ rotates a wheel through an angular displacement of $4.0~\mathrm{rad}$. The work done on the wheel by the torque is一个大小为 $5.0~\mathrm{N \cdot m}$ 的恒定力矩使一个轮子转过 $4.0~\mathrm{rad}$ 的角位移。该力矩对轮子做的功为
A disk of moment of inertia $I$ spins about a vertical axis at angular speed $\omega_0$. A second disk of moment of inertia $2I$, initially at rest, is gently dropped onto the first disk and sticks to it. The final angular speed of the combined disks is一个转动惯量为 $I$ 的圆盘以角速度 $\omega_0$ 绕竖直轴旋转。另一个转动惯量为 $2I$ 的圆盘从静止开始轻轻叠落在第一个圆盘上并与之粘合。两圆盘合并后的最终角速度为
A uniform solid sphere is released from rest at the top of an incline of vertical height $h$ and rolls without slipping to the bottom. Its speed at the bottom is一个均匀实心球从高度为 $h$ 的斜面顶端由静止开始释放，无滑动地滚到底部。到达底部时的速度为
Two satellites orbit the same planet in circular orbits. The orbital radius of satellite 2 is twice that of satellite 1. The ratio $T_2/T_1$ of their orbital periods is两颗卫星在同一行星的圆形轨道上运行。卫星 2 的轨道半径是卫星 1 的两倍。它们的轨道周期之比 $T_2/T_1$ 为
A constant net torque of $4.0~\mathrm{N \cdot m}$ acts on a wheel of moment of inertia $2.0~\mathrm{kg \cdot m^2}$, initially at rest, for $3.0~\mathrm{s}$. The wheel's final angular speed is一个大小为 $4.0~\mathrm{N \cdot m}$ 的恒定合力矩作用在转动惯量为 $2.0~\mathrm{kg \cdot m^2}$ 的轮子上，持续时间 $3.0~\mathrm{s}$，轮子初始静止。轮子的最终角速度为
A uniform solid disk rolls without slipping along a horizontal surface with center-of-mass speed $v$. The fraction of its total kinetic energy that is rotational is一个均匀实心圆盘以质心速度 $v$ 在水平面上无滑动地滚动。其总动能中转动动能所占的比例为
A uniform rod of mass $M$ and length $L$, pivoted at one end and initially at rest, is struck and embedded by a bullet of mass $m$ moving with speed $v$ at the rod's free end (perpendicular to the rod). The angular speed of the rod-plus-bullet system just after the collision is一根质量为 $M$、长度为 $L$ 的均匀细杆，一端铰支，初始静止，被质量为 $m$、速度为 $v$ 的子弹垂直射入其自由端并嵌入其中。碰撞后，杆与子弹组合体的角速度为
A wheel of moment of inertia $0.50~\mathrm{kg \cdot m^2}$ spins at $4.0~\mathrm{rad/s}$. The magnitude of the work that must be done on the wheel to bring it to rest is一个转动惯量为 $0.50~\mathrm{kg \cdot m^2}$ 的轮子以 $4.0~\mathrm{rad/s}$ 旋转。使轮子停止旋转所需做的功的大小为
A horizontal turntable of moment of inertia $I_p = 100~\mathrm{kg \cdot m^2}$ rotates freely about a vertical axis at $\omega_0 = 1.0~\mathrm{rad/s}$. A person of mass $50~\mathrm{kg}$ stands at rest on the turntable at $r = 1.0~\mathrm{m}$ from the axis. The person then walks to the axis (treat the person as a point mass throughout). The new angular speed of the turntable is一个转动惯量为 $I_p = 100~\mathrm{kg \cdot m^2}$ 的水平转台以 $\omega_0 = 1.0~\mathrm{rad/s}$ 绕竖直轴自由旋转。一个质量为 $50~\mathrm{kg}$ 的人静止站在距轴 $r = 1.0~\mathrm{m}$ 处。该人随后走向轴心（全程将人视为质点）。转台的新角速度为
A satellite is placed in a circular orbit such that its orbital period equals one Earth day. Take $GM_\mathrm{E} = 4.0 \times 10^{14}~\mathrm{m^3/s^2}$ and $T_\mathrm{day} = 8.64 \times 10^4~\mathrm{s}$. The orbital radius (measured from Earth's center) is closest to一颗卫星被置于圆形轨道上，使其轨道周期等于地球自转一天。取 $GM_\mathrm{E} = 4.0 \times 10^{14}~\mathrm{m^3/s^2}$，$T_\mathrm{day} = 8.64 \times 10^4~\mathrm{s}$。轨道半径（从地心算起）最接近
A solid sphere, a uniform solid disk, and a thin hoop, all of mass $M$ and radius $R$, are released simultaneously from rest at the top of the same incline and roll without slipping to the bottom. Which arrives first?一个实心球、一个均匀实心圆盘和一个细圆环，质量均为 $M$，半径均为 $R$，同时从同一斜面顶端由静止释放，无滑动地滚到底部。哪个最先到达？
A particle moves in a circular path in the $xy$-plane, traveling counter-clockwise as viewed from the $+z$ axis. Its angular momentum about the center of the circle points in the一个质点在 $xy$ 平面内沿圆形轨道运动，从 $+z$ 轴方向俯视为逆时针。其相对于圆心的角动量指向
A satellite of mass $m$ orbits a planet of mass $M$ in a circular orbit of radius $r$. The total mechanical energy of the satellite is质量为 $m$ 的卫星在质量为 $M$ 的行星的半径为 $r$ 的圆形轨道上运行。卫星的总机械能为
Show all work in the space provided. Partial credit is awarded for correct setup, units, and reasoning. Use $g = 9.8~\mathrm{m/s^2}$ and $G = 6.67 \times 10^{-11}~\mathrm{N \cdot m^2/kg^2}$ unless otherwise stated.请在所提供的空白处写出完整的解题过程。正确的建模、单位和推理均可获得部分分数。除非另有说明，取 $g = 9.8~\mathrm{m/s^2}$，$G = 6.67 \times 10^{-11}~\mathrm{N \cdot m^2/kg^2}$。
A horizontal disk of mass $M = 2.0~\mathrm{kg}$ and radius $R = 0.30~\mathrm{m}$ rotates about a fixed, frictionless vertical axis at angular speed $\omega_0 = 6.0~\mathrm{rad/s}$. A second, identical disk (same $M$, same $R$, axis aligned with the first) is dropped onto the first disk from rest and sticks to it.一个质量为 $M = 2.0~\mathrm{kg}$、半径为 $R = 0.30~\mathrm{m}$ 的水平圆盘以角速度 $\omega_0 = 6.0~\mathrm{rad/s}$ 绕固定的无摩擦竖直轴旋转。另一个完全相同的圆盘（质量、半径相同，轴与第一个圆盘对齐）从静止开始叠落在第一个圆盘上并粘合。
A uniform solid sphere of mass $M = 0.50~\mathrm{kg}$ and radius $R = 0.10~\mathrm{m}$ is released from rest at the top of an incline of angle $\theta = 30^\circ$ and vertical height $h = 0.80~\mathrm{m}$. The sphere rolls without slipping.一个质量为 $M = 0.50~\mathrm{kg}$、半径为 $R = 0.10~\mathrm{m}$ 的均匀实心球从倾角 $\theta = 30^\circ$、竖直高度 $h = 0.80~\mathrm{m}$ 的斜面顶端由静止释放，无滑动地滚动。
A uniform rod of mass $M = 0.50~\mathrm{kg}$ and length $L = 0.80~\mathrm{m}$ is pivoted at one end about a frictionless horizontal axis and hangs vertically at rest. A bullet of mass $m = 0.020~\mathrm{kg}$ moving horizontally at $v_0 = 200~\mathrm{m/s}$ strikes the rod at its free (lower) end and embeds in it.一根质量为 $M = 0.50~\mathrm{kg}$、长度为 $L = 0.80~\mathrm{m}$ 的均匀细杆，一端铰支于无摩擦的水平轴上，竖直悬挂静止。一颗质量为 $m = 0.020~\mathrm{kg}$、以水平速度 $v_0 = 200~\mathrm{m/s}$ 运动的子弹射入杆的自由端（下端）并嵌入其中。
A satellite of mass $m = 500~\mathrm{kg}$ is in a circular orbit of radius $r_1 = 1.5\,R_\mathrm{E}$ around Earth, where $R_\mathrm{E} = 6.4 \times 10^6~\mathrm{m}$ and $M_\mathrm{E} = 6.0 \times 10^{24}~\mathrm{kg}$.质量为 $m = 500~\mathrm{kg}$ 的卫星在半径 $r_1 = 1.5\,R_\mathrm{E}$ 的圆形轨道上围绕地球运行，其中 $R_\mathrm{E} = 6.4 \times 10^6~\mathrm{m}$，$M_\mathrm{E} = 6.0 \times 10^{24}~\mathrm{kg}$。