PART I · SHORT RESPONSE第一部分 · 短答题AP-style MCQ + ON/BC short answer · 18 marksAP 风格选择题 + 安/卑省考短答 · 共 18 分
Section A · Short ResponseA 部分 · 短答题
Mix of multiple-choice and short-answer items. For MCQs, circle the letter; show enough work in the margin that a marker could verify. For short-answer items, state units in every answer. Use $g = 9.8\ \text{m/s}^2$ throughout. No calculator on Q1-Q2; calculator permitted on Q3-Q5.本节包含选择题与短答题。选择题请圈出字母答案，并在空白处写下足以让阅卷人核对的过程。短答题每道都要写出单位。全卷取 $g = 9.8\ \text{m/s}^2$。Q1-Q2 不可使用计算器；Q3-Q5 可用计算器。
A ball on a string moves in a horizontal circle of radius $0.80$ m, completing $5.0$ revolutions per second. What is the speed of the ball? (Use $\pi \approx 3.14$.)一只绳上的球在半径 $0.80$ m 的水平圆上运动，每秒完成 $5.0$ 圈。球的速率是多少？（取 $\pi \approx 3.14$。）
The gravitational force between two spheres is $F$. If the centre-to-centre distance between them is tripled (masses unchanged), what is the new force?两球体之间的引力为 $F$。若它们质心间距变为原来的 $3$ 倍（质量不变），新引力是多少？
A car travels around a flat (unbanked) curve of radius $50$ m. The coefficient of static friction between the tires and the road is $\mu_s = 0.60$. Take $g = 9.8\ \text{m/s}^2$.一辆车在半径 $50$ m 的平坦（无倾斜）弯道上行驶。轮胎与路面间的静摩擦系数为 $\mu_s = 0.60$。取 $g = 9.8\ \text{m/s}^2$。
(a)Show that the maximum speed for rounding the curve without skidding satisfies $v_{\max} = \sqrt{\mu_s g r}$.证明不打滑通过弯道的最大速率满足 $v_{\max} = \sqrt{\mu_s g r}$。[2]
(b)Calculate the maximum speed, with units.计算最大速率，并写出单位。[2]
(c)State whether the maximum speed depends on the mass of the car, and justify briefly.说明最大速率是否依赖于车的质量，并简要论证。[1]
PART II · EXTENDED RESPONSE第二部分 · 简答题AP-feeder FRQ + honors · 34 marksAP 衔接简答题 + 荣誉级 · 共 34 分
Section B · Extended ResponseB 部分 · 简答题
Show every step of reasoning. Draw a free-body diagram and identify which real force points toward the centre before writing $F_{\text{net}} = mv^2/r$. State units in every final answer. Use $g = 9.8\ \text{m/s}^2$ and $G = 6.674 \times 10^{-11}\ \text{N m}^2\text{kg}^{-2}$. Calculator permitted on Q6-Q9.每一步推理都要写出。在写出 $F_{\text{net}} = mv^2/r$ 之前先画受力图并标出指向圆心的真实力。每个最终答案都要写单位。取 $g = 9.8\ \text{m/s}^2$，$G = 6.674 \times 10^{-11}\ \text{N m}^2\text{kg}^{-2}$。Q6-Q9 可用计算器。
Q6MEDIUM中🇺🇸 US美AP-feeder FRQAP 衔接简答题§2 Centripetal force (ball on string)向心力（绳上的球） · HS-PS2-1[8 marks][8 分]
A $0.25$ kg ball is whirled in a horizontal circle of radius $0.50$ m at a constant speed of $4.0$ m/s. The only horizontal force on the ball is the tension in the string.一只 $0.25$ kg 的球以 $4.0$ m/s 的恒定速率在半径 $0.50$ m 的水平圆上旋转。球受到的唯一水平力是绳中的张力。
(a)Find the centripetal acceleration.求向心加速度。[2]
(b)Find the tension in the string.求绳中的张力。[2]
(c)If the speed is doubled to $8.0$ m/s (same radius), find the new tension and state the factor by which it changed.若速率加倍至 $8.0$ m/s（半径不变），求新的张力，并写出张力变化的倍数。[2]
(d)Describe the subsequent motion of the ball if the string suddenly breaks at the instant in part (b).描述若绳在 (b) 时刻突然断裂，球随后的运动。[2]
A roller-coaster car of mass $500$ kg travels through a vertical loop of radius $8.0$ m. Take $g = 9.8\ \text{m/s}^2$.一辆质量 $500$ kg 的过山车通过半径 $8.0$ m 的竖直圆圈。取 $g = 9.8\ \text{m/s}^2$。
(a)At the top of the loop, draw or describe the free-body diagram and write the centripetal-force equation when the normal force is zero.在圆圈最高点，画出或描述受力图，并写出法向力为零时的向心力方程。[2]
(b)Find the minimum speed at the top of the loop.求圆圈最高点的最小速度。[2]
(c)At the bottom of the loop the car's speed is $14$ m/s. Find the normal force the track exerts on the car.在圆圈最低点车的速率为 $14$ m/s。求轨道对车的法向力。[3]
(d)Express the bottom-of-loop normal force as a multiple of the car's weight, and explain the "apparent weight" sensation.将最低点的法向力表示为车重的倍数，并解释"表观重力"的感受。[1]
A rocky planet has mass $M = 6.4 \times 10^{23}$ kg and radius $R = 3.4 \times 10^6$ m. Use $G = 6.674 \times 10^{-11}\ \text{N m}^2\text{kg}^{-2}$.一颗岩质行星的质量 $M = 6.4 \times 10^{23}$ kg，半径 $R = 3.4 \times 10^6$ m。取 $G = 6.674 \times 10^{-11}\ \text{N m}^2\text{kg}^{-2}$。
(a)Find the gravitational field strength $g$ at the planet's surface, with units.求行星表面的引力场强 $g$，并写出单位。[3]
(b)Find the weight of a $50$ kg astronaut standing on the surface.求一名 $50$ kg 宇航员站在地表时的重力。[2]
(c)The astronaut climbs to an altitude equal to one planet radius ($h = R$). Find the gravitational field strength there, without recomputing from scratch (use the inverse-square ratio).宇航员登上等于一个行星半径的高度（$h = R$）。用平方反比比值（无需从头重算）求该处的引力场强。[3]
The International Space Station orbits Earth at an altitude of $h = 400$ km. Use $G = 6.674 \times 10^{-11}\ \text{N m}^2\text{kg}^{-2}$, $M_E = 5.97 \times 10^{24}$ kg, $R_E = 6.37 \times 10^6$ m.国际空间站在 $h = 400$ km 的高度绕地球运行。取 $G = 6.674 \times 10^{-11}\ \text{N m}^2\text{kg}^{-2}$，$M_E = 5.97 \times 10^{24}$ kg，$R_E = 6.37 \times 10^6$ m。
(a)State the orbital radius $r$ (centre-to-centre), making clear it is not the altitude.写出轨道半径 $r$（质心到质心），并说明它不是轨道高度。[1]
(b)By setting gravity equal to the centripetal force, show that the orbital speed is $v = \sqrt{GM_E / r}$.令引力等于向心力，证明轨道速度为 $v = \sqrt{GM_E / r}$。[2]
(c)Calculate the orbital speed, with units.计算轨道速度，并写出单位。[3]
(d)Calculate the orbital period, in minutes.计算轨道周期（以分钟为单位）。[2]
(e)A second satellite of four times the mass orbits at the same radius. State and justify how its speed compares.另一颗质量为四倍的卫星在同一半径上运行。说明并论证它的速度如何比较。[2]
PART III · MODELING / APPLIED第三部分 · 建模与应用AB Diploma + Universal · 28 marks阿省毕业考 + 通用题型 · 共 28 分
Section C · Modeling and ApplicationsC 部分 · 建模与应用
Define symbols (with units) at the start of each question. State the governing equation before substituting. Use $g = 9.8\ \text{m/s}^2$ and $G = 6.674 \times 10^{-11}\ \text{N m}^2\text{kg}^{-2}$. Conclude each question with a one-sentence answer in context. Calculator permitted throughout Part III.每题开始时定义符号（含单位）。代入数值前先写出所用方程。取 $g = 9.8\ \text{m/s}^2$，$G = 6.674 \times 10^{-11}\ \text{N m}^2\text{kg}^{-2}$。每题以一句结合情境的完整句子作答。第三部分全程可用计算器。
Q10MEDIUM中🇨🇦 AB阿AB Diploma-style阿尔伯塔毕业考风格§6 Kepler's Third Law开普勒第三定律 · 20-C1.7k[9 marks][9 分]
Planet Kestrel orbits a Sun-like star at an average orbital radius four times that of Earth around our Sun. Earth's orbital period is $1.0$ year. Both worlds orbit the same star.行星 Kestrel 绕一颗类太阳恒星运行，平均轨道半径是地球绕太阳的四倍。地球的轨道周期为 $1.0$ 年。两者绕同一恒星运行。
(a)State Kepler's Third Law as a ratio relating two bodies orbiting the same star, and explain why $G$ and the star's mass need not be known.写出关联绕同一恒星运行的两个天体的开普勒第三定律比值形式，并解释为何无需知道 $G$ 和恒星质量。[3]
(b)Find the orbital period of Kestrel, in years.求 Kestrel 的轨道周期（以年为单位）。[3]
(c)A third planet has a period of $27$ Earth-years. Find its orbital radius as a multiple of Earth's.第三颗行星的周期为 $27$ 个地球年。求其轨道半径相当于地球的几倍。[3]
A newly discovered exoplanet has mass $M = 8.0 \times 10^{24}$ kg and radius $R = 7.0 \times 10^6$ m. Use $G = 6.674 \times 10^{-11}\ \text{N m}^2\text{kg}^{-2}$.一颗新发现的系外行星质量 $M = 8.0 \times 10^{24}$ kg，半径 $R = 7.0 \times 10^6$ m。取 $G = 6.674 \times 10^{-11}\ \text{N m}^2\text{kg}^{-2}$。
(a)Starting from $mg = GmM/R^2$, derive the expression $g = GM/R^2$ for the surface gravitational acceleration.从 $mg = GmM/R^2$ 出发，推导表面重力加速度的表达式 $g = GM/R^2$。[2]
(b)Calculate the surface gravitational acceleration, with units.计算表面重力加速度，并写出单位。[3]
(c)Find the weight of a $60$ kg lander on the surface.求一台 $60$ kg 着陆器在地表的重力。[2]
(d)State, with a one-sentence reason, whether the lander would weigh more or less here than on Earth.用一句话说明该着陆器在此处比在地球上更重还是更轻，并给出理由。[2]
Q12HARD难Honors荣誉级🇺🇸 US美AP-feeder FRQAP 衔接简答题§7 Mass from orbital data由轨道数据求质量 · HS-PS2-4 (above two-body floor)（超出两体基准）[10 marks][10 分]
A moon orbits a distant planet in a circular orbit of radius $r = 1.9 \times 10^7$ m with a period of $T = 1.5$ Earth-days. Use $G = 6.674 \times 10^{-11}\ \text{N m}^2\text{kg}^{-2}$ and $1\ \text{day} = 86\,400$ s.一颗卫星以半径 $r = 1.9 \times 10^7$ m 的圆形轨道绕一颗遥远的行星运行，周期为 $T = 1.5$ 个地球日。取 $G = 6.674 \times 10^{-11}\ \text{N m}^2\text{kg}^{-2}$，$1\ \text{天} = 86\,400$ s。
(a)By equating gravity and centripetal force for the moon, derive the expression $M = 4\pi^2 r^3 / (G T^2)$ for the planet's mass.通过令卫星的引力等于向心力，推导行星质量表达式 $M = 4\pi^2 r^3 / (G T^2)$。[3]
(b)Convert the period to seconds.将周期换算为秒。[1]
(c)Calculate the mass of the planet, with units.计算行星的质量，并写出单位。[4]
(d)Explain why the mass of the orbiting moon does not appear in your result.解释为何绕行卫星的质量不出现在结果中。[2]
🇺🇸 US NGSS美国 NGSSHS-PS2-1 · HS-PS2-4
🇨🇦 Ontario安大略SPH4U Strand B · Strand D
🇨🇦 British Columbia不列颠哥伦比亚Physics 12: circular motion, gravitation, satellite motion物理 12：圆周运动、万有引力、卫星运动
🇨🇦 Alberta阿尔伯塔Physics 20 Unit B · Unit C · 20-B2.2k · 20-C1.2k · 20-C1.5k
Full Syllabus Map lives in ../Study Guides/Unit_5_Circular_Motion_and_Gravitation.html. Note: orbits and Kepler's laws (Q9, Q12) are core for ON SPH4U / BC Physics 12 / AB Physics 20 but sit above the NGSS-assessed floor (HS-PS2-4 is limited to two-object systems), so those items carry an Honors flag on the US track.完整大纲对照表见 ../Study Guides/Unit_5_Circular_Motion_and_Gravitation.html。注：轨道与开普勒定律（Q9、Q12）为安大略 SPH4U / 卑诗物理 12 / 阿省物理 20 的核心内容，但超出 NGSS 考查范围（HS-PS2-4 限于两物体系统），故在美国轨道上标注荣誉级。