AP-Style Practice QuestionsAP 风格练习题
Topics主题 5.1 - 5.6MECH
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.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 $g = 9.8~\mathrm{m/s^2}$。
A wheel rotates at $60~\mathrm{rev/min}$. Its angular speed in $\mathrm{rad/s}$ is一个轮子以 $60~\mathrm{rev/min}$ 旋转。其角速度（单位 $\mathrm{rad/s}$）为
A point on the rim of a disk of radius $0.50~\mathrm{m}$ moves with the disk at angular speed $\omega = 4.0~\mathrm{rad/s}$. The linear speed of that point is半径为 $0.50~\mathrm{m}$ 的圆盘边缘上一点随圆盘以角速度 $\omega = 4.0~\mathrm{rad/s}$ 转动。该点的线速度为
A force of $20~\mathrm{N}$ is applied perpendicular to the handle of a wrench at a distance $0.30~\mathrm{m}$ from the axis of rotation. The magnitude of the torque about the axis is一个 $20~\mathrm{N}$ 的力垂直作用于扳手手柄，作用点距转动轴 $0.30~\mathrm{m}$。关于该轴的力矩大小为
The moment of inertia of a thin uniform rod of mass $M$ and length $L$ about an axis through its center, perpendicular to the rod, is质量为 $M$、长度为 $L$ 的细均匀杆，绕过其中心且垂直于杆的轴的转动惯量为
A wheel initially rotating at $\omega_0 = 2.0~\mathrm{rad/s}$ undergoes a constant angular acceleration $\alpha = 4.0~\mathrm{rad/s^2}$ for $3.0~\mathrm{s}$. Its final angular speed is一个轮子初始角速度为 $\omega_0 = 2.0~\mathrm{rad/s}$，以匀角加速度 $\alpha = 4.0~\mathrm{rad/s^2}$ 转动 $3.0~\mathrm{s}$。其末角速度为
A disk of radius $0.20~\mathrm{m}$ rotates about its central axis at constant angular speed $\omega = 10~\mathrm{rad/s}$. The centripetal acceleration of a point on the rim is半径为 $0.20~\mathrm{m}$ 的圆盘绕中心轴以匀角速度 $\omega = 10~\mathrm{rad/s}$ 转动。圆盘边缘上一点的向心加速度为
A force of $30~\mathrm{N}$ is applied at the end of a wrench of length $0.40~\mathrm{m}$, but at an angle of $30^\circ$ to the wrench handle. The magnitude of the torque about the axis is一个 $30~\mathrm{N}$ 的力施加在长 $0.40~\mathrm{m}$ 的扳手末端，方向与扳手柄成 $30^\circ$ 角。关于轴的力矩大小为
A solid uniform disk of mass $M$ and radius $R$ rotates about an axis perpendicular to the disk through a point on its edge. Its moment of inertia about that axis is质量为 $M$、半径为 $R$ 的实心均匀圆盘，绕过其边缘上一点且垂直于圆盘的轴转动。关于该轴的转动惯量为
A uniform horizontal beam of mass $10~\mathrm{kg}$ and length $4.0~\mathrm{m}$ is hinged at the wall at one end. The far end is supported by a vertical cable. The tension in the cable is一根质量为 $10~\mathrm{kg}$、长 $4.0~\mathrm{m}$ 的均匀水平梁，一端用铰链固定在墙上，另一端由竖直绳索支撑。绳索中的张力为
A net torque of $6.0~\mathrm{N \cdot m}$ acts on a wheel with moment of inertia $I = 2.0~\mathrm{kg \cdot m^2}$. The wheel's angular acceleration is一个合力矩 $6.0~\mathrm{N \cdot m}$ 作用在转动惯量 $I = 2.0~\mathrm{kg \cdot m^2}$ 的轮子上。该轮子的角加速度为
A wheel starts from rest and undergoes constant angular acceleration $\alpha = 2.0~\mathrm{rad/s^2}$. Its angular displacement after $5.0~\mathrm{s}$ is一个轮子从静止开始，以匀角加速度 $\alpha = 2.0~\mathrm{rad/s^2}$ 转动。$5.0~\mathrm{s}$ 后的角位移为
A thin hoop, a solid disk, and a solid sphere all have the same mass $M$ and the same radius $R$, and rotate about axes through their centers. Ranked from greatest to least moment of inertia, they are一个细圆环、一个实心圆盘和一个实心球体，质量均为 $M$，半径均为 $R$，均绕通过各自中心的轴转动。按转动惯量从大到小排列，顺序为
A net torque $\tau$ acts on a uniform solid disk of mass $M$ and radius $R$ about its central axis. The angular acceleration of the disk is合力矩 $\tau$ 作用于质量为 $M$、半径为 $R$ 的均匀实心圆盘的中心轴上。圆盘的角加速度为
Two masses, $m_1 = 4.0~\mathrm{kg}$ and $m_2 = 2.0~\mathrm{kg}$, are connected by a massless string passing over a uniform-disk pulley of mass $M = 4.0~\mathrm{kg}$ and radius $R$. The string does not slip on the pulley. Take $g = 10~\mathrm{m/s^2}$. The acceleration of the masses is closest to两个质量 $m_1 = 4.0~\mathrm{kg}$ 和 $m_2 = 2.0~\mathrm{kg}$ 通过无质量绳索跨过质量为 $M = 4.0~\mathrm{kg}$、半径为 $R$ 的均匀圆盘滑轮相连。绳索在滑轮上不打滑。取 $g = 10~\mathrm{m/s^2}$。两质量的加速度最接近
A uniform ladder of mass $M$ leans at angle $\theta$ above the horizontal against a frictionless vertical wall. The coefficient of static friction between the ladder and the floor is $\mu$. The minimum value of $\theta$ for which the ladder does not slip is given by质量为 $M$ 的均匀梯子以与水平面成 $\theta$ 角靠在无摩擦的竖直墙壁上。梯子与地面之间的静摩擦系数为 $\mu$。梯子不滑动的最小 $\theta$ 值满足
A point mass $m$ is rigidly attached to one end of a uniform rod of mass $M$ and length $L$. The system rotates about an axis through the rod's free end (i.e. the end opposite the point mass), perpendicular to the rod. Its moment of inertia about that axis is质量为 $m$ 的质点固定在质量为 $M$、长度为 $L$ 的均匀杆的一端。该系统绕过杆的自由端（即与质点相对的一端）且垂直于杆的轴转动。关于该轴的转动惯量为
A force $\vec F = 3\,\hat\jmath~\mathrm{N}$ is applied at the position $\vec r = 2\,\hat\imath~\mathrm{m}$ relative to a fixed pivot. The torque about that pivot is一个力 $\vec F = 3\,\hat\jmath~\mathrm{N}$ 施加在相对于固定转轴位置为 $\vec r = 2\,\hat\imath~\mathrm{m}$ 处。关于该转轴的力矩为
A uniform solid disk of mass $M$ and radius $R$ has a light cord wrapped around it; the upper end of the cord is fixed. The disk is released from rest and falls vertically as the cord unwinds. The downward acceleration of the disk's center is质量为 $M$、半径为 $R$ 的均匀实心圆盘上绕有一轻绳，绳的上端固定。圆盘从静止开始释放，随绳展开竖直下落。圆盘中心的向下加速度为
Show all work in the space provided. Partial credit is awarded for correct setup, units, and reasoning. Use $g = 9.8~\mathrm{m/s^2}$ unless otherwise stated.请在所提供的空白处写出所有解题过程。正确的建模、单位和推理均可获得部分分数。除非另有说明，使用 $g = 9.8~\mathrm{m/s^2}$。
A uniform-disk pulley of mass $M = 2.0~\mathrm{kg}$ and radius $R = 0.10~\mathrm{m}$ has its axis fixed and frictionless. A light cord is wrapped around the pulley; a block of mass $m = 1.0~\mathrm{kg}$ hangs from the other end. The cord does not slip. The system is released from rest.质量为 $M = 2.0~\mathrm{kg}$、半径为 $R = 0.10~\mathrm{m}$ 的均匀圆盘滑轮，其轴固定且无摩擦。一轻绳绕在滑轮上，另一端悬挂质量为 $m = 1.0~\mathrm{kg}$ 的物块。绳索不打滑。系统从静止开始释放。
A uniform horizontal beam of mass $M = 20~\mathrm{kg}$ and length $L = 4.0~\mathrm{m}$ is attached to a wall by a frictionless hinge at one end. The far end of the beam is supported by a light cable that runs from the far end of the beam upward to the wall, making an angle of $30^\circ$ above the horizontal beam. A point load of mass $m = 10~\mathrm{kg}$ hangs from the far end of the beam.质量为 $M = 20~\mathrm{kg}$、长 $L = 4.0~\mathrm{m}$ 的均匀水平梁，一端通过无摩擦铰链固定在墙上。梁的远端由一根轻绳支撑，绳从梁的远端向上连接到墙壁，与水平梁成 $30^\circ$ 角。质量为 $m = 10~\mathrm{kg}$ 的集中载荷悬挂在梁的远端。
A uniform rod of mass $M = 0.40~\mathrm{kg}$ and length $L = 1.20~\mathrm{m}$ has a small point mass $m = 0.10~\mathrm{kg}$ rigidly attached to one end. The rod is free to rotate about a frictionless pivot at the opposite end (so the heavy end is far from the pivot). The rod is held in a horizontal position and released from rest.质量为 $M = 0.40~\mathrm{kg}$、长 $L = 1.20~\mathrm{m}$ 的均匀杆，在一端固定连接一个质量为 $m = 0.10~\mathrm{kg}$ 的小质点。杆可绕另一端的无摩擦枢轴自由转动（即重端远离枢轴）。杆保持水平位置，从静止释放。
A uniform solid cylinder of mass $M$ and radius $R$ rolls without slipping down an incline of angle $\theta$.质量为 $M$、半径为 $R$ 的均匀实心圆柱体，在倾角为 $\theta$ 的斜面上做无滑动滚动。