国外物理试题

国外大学物理考试题目及答案一、选择题（每题2分，共10分）1. 光在真空中的传播速度是多少？A. 3×10^8 m/sB. 3×10^4 m/sC. 3×10^2 m/sD. 3×10^6 m/s答案：A2. 根据牛顿第二定律，力和加速度之间的关系是什么？A. F = maB. F = m/vC. F = a/mD. F = v/a答案：A3. 一个物体的质量为2kg，受到10N的力，它的加速度是多少？A. 5 m/s²B. 4 m/s²C. 3 m/s²D. 2 m/s²答案：A4. 哪种类型的原子核反应可以释放出大量的能量？A. 核裂变B. 核聚变C. 放射性衰变D. 核融合答案：A5. 一个电路中的电阻为6Ω，电流为2A，那么电压是多少？A. 6VB. 12VC. 24VD. 36V答案：B二、计算题（每题10分，共30分）1. 一辆汽车以60 km/h的速度向东行驶，同时有一股西风以30 km/h 的速度吹。

如果汽车关闭发动机，它将受到风的影响，请问汽车的实际速度是多少？答案：汽车的实际速度是30 km/h，方向向东。

因为汽车关闭发动机后，它的速度将与风速相反，但由于风向与汽车行驶方向相反，所以实际速度是两者之差。

2. 一个质量为0.5kg的物体从静止开始自由下落，忽略空气阻力，求物体下落2秒后的速度和位移。

答案：物体下落2秒后的速度是 v = gt = 9.8 m/s² × 2 s = 19.6 m/s。

位移是s = 1/2 × g × t² = 1/2 × 9.8 m/s² × (2 s)² = 19.6 m。

3. 一个电路包含一个12V的电池和一个8Ω的电阻。

如果电路中的电流是1.5A，那么电路中的总电阻是多少？答案：根据欧姆定律，电压V = IR，所以电阻R = V/I = 12V /1.5A = 8Ω。

10th International Physics Olympiad1977, Hradec Kr´alov´e, Czechoslovakia Problem 1.The compression ratio of a four-stroke internal combustion engine is The engine draws in air and gaseous fuel at a temperature 27o C at a pressure 1 atm = 100 kPa. Compression follows an adiabatic process from point 1 to point 2, see Fig. 1. The pressure in the cylinder is doubled during the mixture ignition (2–3). The hot exhaust gas expands adiabatically to the volume V2 pushing the piston downwards (3–4). Then the exhaust valve opens and the pressure gets back to the initial value of 1 atm. All processes in the cylinder are supposed to be ideal. The Poisson constant (i.e. the ratioof specific heats C p=C V ) for the mixture and exhaust gas is (Thecompression ratio is the ratio of the volume of the cylinder when the piston is at the bottom to the volume when the piston is at the top.)a) Which processes run between the points 0–1, 2–3, 4–1, 1–0?b) Determine the pressure and the temperature in the states 1, 2, 3 and 4.c) Find the thermal efficiency of the cycle.d) Discuss obtained results. Are they realistic?Solution: a) The description of the processes between particular points is the following:0–1 : intake stroke isobaric and isothermal process1–2 : compression of the mixture adiabatic process2–3 : mixture ignition isochoric process3–4 : expansion of the exhaust gas adiabatic process4–1 : exhaust isochoric process1–0 : exhaust isobaric processLet us denote the initial volume of the cylinder before induction at the point 0 by V1, after induction at the point 1 by V2 and the temperatures at the particular points by T0, T1, T2, T3 and T4.b) The equations for particular processes are as follows.0–1 : The fuel-air mixture is drawn into the cylinder at the temperature of T0 = T1 = 300 K and a pressure of p0 = p1 = 0:10 MPa.1–2 : Since the compression is very fast, one can suppose the process to be adiabatic. Hence:From the first equation one obtainsand by the dividing of both equations we arrive after a straightforward calculation atFor given values,, p1 = 0:10 MPa, T1= 300 K we have p2= 2:34 MPa and T2 = 738 K(t2 = 465o C).2–3 : Because the process is isochoric and p3 = 2p2 holds true, we can writec) Thermal efficiency of the engine is defined as the proportion of the heat supplied that is converted to net work. The exhaust gas does work on the piston during the expansion 3–4, on the other hand, the work is done on the mixture during the compression 1–2. No work is done by/on the gas during the processes 2–3 and 4–1. The heat is supplied to the gas during the process 2–3.The net work done by 1 mol of the gas isd) Actually, the real pV -diagram of the cycle is smooth, without the sharp angles. Since the gas is not ideal, the real efficiency would be lower than the calculated one. Problem 2.Dipping the frame in a soap solution, the soap forms a rectangle film of length b andheight h. White light falls on the film at an angle (measured with respect to thenormal direction). The reflected light displays a green color of wavelengtha) Find out if it is possible to determine the mass of the soap film using the laboratory scales which has calibration accuracy of 0.1 mg.b) What color does the thinnest possible soap film display being seen from the perpendicular direction? Derive the related equations.b) If the light falls at the angle of 30o then the film seen from the perpendicular direction cannot be colored. It would appear dark.Problem 3.An electron gun T emits electrons accelerated by a potential difference U in a vacuum in the direction of the line a as shown in Fig. 2. The target M is placed at a distance d from the electron gun in such a way that the line segment connecting the points T andM and the line a subtend the angle as shown in Fig. 2. Find the magneticinduction B of the uniform magnetic fieldSolution: a) If a uniform magnetic field is perpendicular to the initial direction of motion of an electron beam, the electrons will be deflected by a force that is always perpendicular to their velocity and to the magnetic field. Consequently, the beam will be deflected into a circular trajectory. The origin of the centripetal force is the Lorentz force, sob) If a uniform magnetic field is neither perpendicular nor parallel to the initial direction of motion of an electron beam, the electrons will be deflected into a helical trajectory. Namely, the motion of electrons will be composed of an uniform motion on a circle in the plane perpendicular to the magnetic field and of an uniformrectilinear motion in the direction of the magnetic field. The component of theinitial velocity , which is perpendicular to the magnetic field (see Fig. 4), willmanifest itself at the Lorentz force and during the motion will rotate uniformly aroundthe line parallel to the magnetic field. The component parallel to the magneticfield will remainHence we can calculate the radius of the circular trajectory。

英文版物理题以下就是小编给大家盘点的英文版物理题，仅供大家参考。

以下是一些英文版物理题：1.A50kg block is resting on a frictionless horizontal surface.A force of100N is applied to the block in the horizontal direction.What is the acceleration of the block?2.An object is thrown vertically upwards with an initial velocity of20m/s.忽略空气阻力，计算该物体达到最高点所需的时间和高度。

3.A ball is thrown horizontally with a velocity of10m/s from a height of5m.Calculate the horizontal distance the ball travels before hitting the ground.4.A10kg mass is attached to a spring with a spring constant of50N/m.The mass is displaced 0.2m from its equilibrium position and released. Calculate the maximum speed of the mass as it oscillates back and forth.5.A current of5A flows through a resistor witha resistance of10Ω.Calculate the potential difference across the resistor.These are just a few examples of英文版物理题.The specific questions and topics will depend on the level of physics and the course curriculum.。

英语物理试题及答案一、选择题（每题2分，共20分）1. Which of the following is the unit of force in the International System of Units (SI)?A. NewtonB. JouleC. WattD. Coulomb2. What is the speed of light in a vacuum?A. 299,792 kilometers per secondB. 299,792 meters per secondC. 299,792 miles per hourD. 299,792 feet per second3. The formula for calculating work done in physics is:A. Work = Force × DistanceB. Work = Force × TimeC. Work = Mass × AccelerationD. Work = Force × Velocity4. Which of the following is not a fundamental force in nature?A. Gravitational forceB. Electromagnetic forceC. Nuclear forceD. Frictional force5. The principle of conservation of energy states that:A. Energy can be created or destroyed.B. Energy can neither be created nor destroyed.C. Energy can only be transformed from one form to another.D. Energy can be transformed and destroyed.6. What is the formula for calculating the kinetic energy ofan object?A. KE = 1/2 mv^2B. KE = 1/2 mvC. KE = mv^2D. KE = mv7. The law of reflection states that:A. The angle of incidence is equal to the angle of reflection.B. The angle of incidence is greater than the angle of reflection.C. The angle of incidence is less than the angle ofreflection.D. The angle of reflection is always 90 degrees.8. What is the primary difference between a conductor and an insulator?A. Conductors have a higher resistance than insulators.B. Conductors allow the flow of electric current, while insulators do not.C. Insulators have a higher resistance than conductors.D. Conductors are made of metals, while insulators are not.9. The formula for calculating the electric power is:A. Power = Voltage × CurrentB. Power = Voltage / CurrentC. Power = Current^2 / VoltageD. Power = Voltage^2 / Current10. The relationship between wavelength, frequency, and speed of light is given by the equation:A. Speed = Wavelength × FrequencyB. Speed = Wavelength / FrequencyC. Speed = 1 / (Wavelength × Frequency)D. Speed = Frequency / Wavelength二、填空题（每题2分，共20分）1. The SI unit for electric current is the ________.2. The process of an object moving from a higher potential energy to a lower potential energy is called ________.3. The formula for calculating the gravitational force between two objects is ________.4. The SI unit for electric charge is the ________.5. The formula for calculating the electric field strength is ________.6. The principle that states that for every action, there is an equal and opposite reaction is known as ________.7. The formula for calculating the magnetic force on a current-carrying wire is ________.8. The SI unit for temperature is the ________.9. The process of converting electrical energy into other forms of energy is called ________.10. The formula for calculating the capacitance of a parallel plate capacitor is ________.三、简答题（每题10分，共30分）1. Explain the difference between a transverse wave and a longitudinal wave.2. Describe the process of photosynthesis in plants.3. Discuss the concept of the Doppler effect and its applications.四、计算题（每题15分，共30分）1. A 5 kg object is moving at a velocity of 10 m/s. Calculate its kinetic energy.2. A 10 m long wire carries a current of 5 A. If the wire is placed in a magnetic field with a strength of 0.2 T,calculate the magnetic force acting on the wire.五、实验题（每题20分，共20分）1. Design an experiment to demonstrate the principle of the conservation of momentum. Include the materials needed, the procedure, and the expected results.答案：一、选择题1. A2. B3. A4. D5. B6. A7. A8. B9. A10. A二、填空题1. Ampere2. Energy conversion3. F = G * (m1 * m2) / r^2 (where F is the gravitational force, G is the gravitational constant, m1 and m2 are the masses of the objects, and r is the distance between their centers)4. Coulomb5. E = F / q (where E is the。

大学物理试题(国外英文资料)College physics examination questionsFirst, the multiple-choice questions: (39 points)1. (3 points)The acceleration of a particle moving at a radius of R is the magnitude of the acceleration (V means the velocity of a particle at any time)(A) (B)(C) (D) [[]]2. (3 points)An object of mass m falls from the air and is affected by gravity as well as a resistance proportional to the square of velocity. The coefficient of proportionality is k, and K is the normal number. The closing velocity of the falling object (i.e., the speed at which the final object moves at uniform speed) will be(A) (B)(C) GK (D) [[]]3. (3 points)A spring oscillator of M quality is placed horizontally at rest in equilibrium. As shown, a bullet with a mass of M is injected into the oscillator at a horizontal velocity and then moved along with it. If the level is smooth, then the maximum potential energy of the spring is(A) (B)(C) (D) [[]]4. (3 points)A child of the quality of M stands on the edge of a horizontal platform with a radius of R. The platform can rotate freely through a vertical, smooth, fixed axis through its center. The moment of inertia is J. Both the platform and the child are stationary at the start. When the child suddenly moves counter clockwise toward the edge of the platform at a rate of V relative to the ground, the angular velocity and the rotation direction of the platform relative to the ground are(A) clockwise.(B) counter clockwise.(C) clockwise.(D) counter clockwise. [...]5. (3 points)Two different ideal gases, if their most probable rates are equal, their(A) equal to the average rate, root mean square speed equal.(B) equal to the average rate, root mean square speed is not equal.(C) the average rate is not equal, the root mean square speed equal.(D) the average rate is not equal, not equal to the root mean square speed. [...]6. (3 points)According to the second law of thermodynamics:(A) work can be converted to heat, but heat can not be converted to power.(B) heat can be transferred from a hot object to a cryogenic substance, but not from a cryogenic object to a high temperature object.(C) irreversible processes are processes that cannot proceed in the opposite direction.(D) all spontaneous processes are irreversible. [...]7. (3 points)There are several explanations for the interpretation of Gauss's theorem:(A) if the Gauss surface is zero everywhere, there is no charge in the plane.(B) if the Gauss surface has no charge, then the Gauss surface is zero everywhere.(C) if there is no zero on the Gauss surface, there must be charges in the Gauss plane.(D) if there is a net charge in the Gauss plane, the electric flux through the Gauss surface must not be zero.(E) Gauss's theorem applies only to electric fields with high symmetry. [...]8. (3 points)The radius of the cross section of a long straight wire is a, and a thin cylinder with a radius of B is coaxially arranged outside the conductor, and the two of them are insulated from each other. And the outer cylinder is grounded as shown. The electric charge per unit length of the wire is +, and the potential of the earth is zero. Then the field strength and the electric potential of the P point (Op=r) between the twoconductors are respectively:(A)(B)(C)(D) [[]]9. (3 points)The square coils with side lengths are respectively represented by two modes of current I (wherein the AB and CD are coplanar with the square), and in these two cases, the magnetic induction intensity of the coil at the center of the coil is respectively(A)(B)(C)(D) [[]]10. (3 points)The picture shows four charged particles in the same direction perpendicular to the magnetic field line, and the deflection trajectory of the magnetic field is injected into the uniformmagnetic field. The direction of the magnetic field is perpendicular to the surface of the O,The trajectory of the four particles is equal in mass and the magnitude of the electric energy is equal. In that case, the trajectory of the negatively charged particles with the largest kinetic energy is(A) Oa (B) Ob(C) Oc (D) Od [...]11. (3 points)A mass of simple harmonic vibration on the X axis, the amplitude of A = 4cm, T = 2S cycle, its equilibrium position is taken as the origin of coordinates, if t=0 the first moment of the particle by x= 2cm, and to the negative direction of X axis motion is second 2cm particle by x= at the moment(A) 1s (B) (2/3) s(C) (4/3) s (D) 2S [[]]12. (3 points)Using wedge interference method can detect surface defects, when the wavelength of monochromatic parallel light vertical incident, if the interference fringes observed as shown in the figure, each part of the fringe vertex exactly with left fringeof the straight part of the tangent line, then the surface of the workpiece and bending at the corresponding part of the fringe(A) raised, and the height is (B) raised, and the height is...(C) depressions, and the depth is (D) depressions, and the depth is []13. (3 points)A beam of light is a mixture of natural light and polarized light, let it through a vertical polarizer, if this incident beam axis rotating polarizer, the measured transmission light intensity maximum is 5 times the minimum value, then the incident beam in natural light and polarized light intensity ratio is(A) 1 / 2 (B) 1 / 5(C) 1 / 3 (D) 2 / 3Two, fill in the blanks: (46 points)1. (3 points)Let the particles move along the X axis. When the initial condition is t=0, the initial velocity is v0=0, and the coordinate x0=10 is a=4t. Then the equation of motion is.2. (3 points)Under the action of constant force F, an object moves in a straight line. The equation of motion is x=A-Bt+ct2 (A, B, C is constant), and the mass of the object should be m=.3. (3 points)At a constant speed, the quality of M ship, respectively, forward and backward at the same time the level of two throws of equal mass (m) objects thrown two objects relative to the ship the same rate (U) expression of the ship and try to write in the process of the system of the law of conservation of momentum (don't have Jane, for reference).4. (5 points)As shown in the figure, a homogeneous consolidation in a thin rod end ball, and can rotate around a horizontal smooth fixed shaft O to rotate, there is a bullet along with the horizontal angle direction and embedded in the ball hit, then hit in the process of conservation, cricket, bullets, rod system, the reason is. The process of cricket bat and ball increased after being hit in the conservation on cricket, bullets, rod, earth system.5. (3 points)At room temperature, the pressure of the ideal gas of 1 moldiatomic molecules is P, and the volume is V, and the average kinetic energy of the gas molecule is.6. (3 points)If the pressure and volume of an ideal gas remain constant, but the mass and temperature change, then can the internal energy change?.7. (3 points)The thermodynamic temperature of a high temperature heat source is n times of the thermodynamic temperature of a low temperature heat source. In a Kano cycle, the heat delivered by a gas to a cryogenic heat source is twice as much as that obtained from a high temperature heat source.8. (3 points)A simple harmonic wave propagates along the positive direction of the X axis. The relation curves between the vibration velocity and time at two points of X1 and X2 are shown as follows (a) and (b), and the distance between X1 and X2 is known as (lambda lambda).9. (3 points)White light (4000-7000) vertical incidence of 4000 slits per centimeter of grating, can produce the level of the complete visible spectrum.10. (3 points)A charged metal ball, when it is surrounded by a vacuum, stores the electrostatic energy of Wo and keeps its energy constant,It is immersed in an infinite isotropic homogeneous dielectric with relative dielectric constant, when its electrostatic energy is We =.11. (6 points)The three basic assumptions of Bohr's theory of hydrogen atoms are:(1),(2),(3).12. (5 points)An electron at a rate of motion of 0.99c (electron rest mass of 9.11 * 1031kg), then the total electron energy is J, the kinetic energy of classical mechanics and relativistic electron kinetic energy ratio.13. (3 points)Static mass is me the potential for electronic, electrostaticfield accelerated U12, without considering the effect of relativity, the De Broglie wavelength lambda = E.Three. Calculation questions: (65 points)1. (10 points)The equation of motion of a known particle is (as a constant),Find (1) the trajectory equation and velocity of the particle(2) the velocity of a particle and the rotation direction ofa particle(3) the relation between the acceleration of a particle and the vector?2. (10 points)M was a short tube, with a length of hard straight rod suspension as shown in figure L, quality can be ignored, with ether droplets Sheng tube, pipe with mass m cork closed, when the heating tube cork in the ether vapor pressure to fly out, hanging around the tube O in the vertical plane for a complete circular motion, then the minimum speed of the cork flew out for? If you change a hard straight pole into a string, what if?3. (10 points)Having two concentric spherical shells with a radius of insulation for each other, and when the + Q is given to the inner ball:(1) the charge distribution and electric potential of the outer sphere;(2) re insulating the ball after grounding, the charge distribution and the electric potential of the outer sphere(3) then, the inner sphere is grounded, the charge distribution of the inner sphere and the potential of the outer sphere4. (10 points)As shown in the figure, the plane charged ring two coplanar, the inner and outer radius are respectively R1, R2 and R2, R3, the outside of the ring to a second N2 RPM clockwise, inside the ring to a second N1 rpm counterclockwise. If the charge surface density is the ratio of the N1 to the N2, the magnetic induction intensity at the center of the circle is zero.5. (10 points)As shown in the figure, the current long straight conductor for I, a B C D rectangular frame with a long straight conductorcoplanar, and the a D A D C / B a B edge D side is fixed, a and C B to speed without friction uniform translational t=0, a, B and C D side edge coincidence, set line inductance negligible.(1) for example, i=I0, seek the electromotive force in a B, a, B, two points, which point has high potential?(2) the total induced electromotive force in the wire frame when the a b t is moved to the position shown by i=I0cos omega.6. (10 points)A plane harmonic wave propagates along the negative direction of the Ox axis, the wavelength is lambda, and the vibration law of the particle at P is shown in figure.(1) seeking the vibration equation of particle at P;(2) find the wave equation of this wave;(3) in the figure, the vibration equation of the particle at the coordinate origin O is calculated.7. (5 points)In the experiment of single slit Fraunhofer diffraction for white, second bright fringe center is measured at the wavelength of third level bright fringe center and thewavelength for the red wavelength for overlap.Second pageThree hundred and thirty-oneSouth China University of TechnologyIn 2004, I studied the master's degree entrance examination papers(the answer to the test paper is invalid. Please answer it on the answer sheet. After the test, this volume must be returned with the answer sheet.)Subject name: General PhysicsApplicable profession: Philosophy of science and technology Common pageFirst page。

bpho英国物理竞赛题目
以下是BPhO英国物理竞赛的部分题目：
1. 题目：一个钢球以30ms-1的速度从的高度扔到坚硬的表面上。

它在每次反弹时保留了70%的能量。

计算: (i) 物体第一次落地时的速度; (ii) 物体在反弹4次后达到的最大高度。

2. 题目：一个长途自行车手使用的自行车电脑是双动力的:它有一个内部电池和一个太阳能电池板。

3. 题目：圆柱体内装着n种不同体积的液体，这些液体形成水平层，每层的高度为h。

(ii)在围绕第二液体的表面A上的力F1是多少? (iii)给出对圆柱体底部Fn液体表面A第n小块的液体，底部的压力F1的表达式?
4. 题目：(iii)求出火箭加速度与时间的函数t的表达式，给定T，g，mt，m0和推力作用的总时间t0。

(iv)计算发射后宇航员的体重翻倍的时间。

希望以上信息对您有所帮助，如果您还有其他问题，欢迎告诉我。

历届国际物理奥林匹克竞赛试题与解答第8届（1975年于德意志民主共和国的居斯特罗）【题1】一根杆以恒定的角速度ω绕竖直轴旋转，杆与轴的夹角为（900－α）。

质量为m 的质点可以沿杆滑动，摩擦系数为μ 。

求转动过程中，质点保持在同一高度的条件（如图8.1）。

解：我们发现，采用所谓“滑动摩擦角”概念是有用的。

如果滑动摩擦系数等于某一角度的正切值，就称这个角ε为“滑动摩擦角”（如解图8.1所示），即tan ε＝μ我们必须求出把物体压向平台的合力。

如果合力与平面法线之间的夹角在滑动摩擦角之内，则摩擦力大到足以阻止运动。

极限情形是合力与摩擦角的一臂重合。

对于本题，当我们寻找质点在旋转杆上向上滑动的极限情况时，合力应位于（α＋ε）角的双臂内（如解图8.2所示）。

图8.1ε解图8.1 解图8.2把质点压在杆上的力是重力mg 与m ω2r ＝m ω2L cos α的合力。

故质点在向上滑动的极限情形下，角（α＋ε）的正切为gL mg L m αωαωεαcos cos )tan(22==+ 同理，质点向下滑动的极限情形可用角（α＋ε）的正切得到。

于是，如果)tan(cos )tan(2εααωεα+≤≤g L －则质点在旋转杆上处于平衡。

从边界条件可以看出，存在着一个较高位置（L f ）和一个较低位置（L a ），质点在这两位置之间的任何地方将处于随遇解图8.3平衡状态。

在这两边界之外，质点无法平衡，质点将向上或向下滑动。

随遇平衡位置L f －L a 可由边界条件导出：)tan tan 1(cos tan 22232εααωε⋅-=-g L L a f 解图8.3对不同的α角，画出质点在杆上哪些部分处于随遇平衡，（取ω＝10 s -1，μ＝0.268，ε＝150）。

虚线表示无摩擦时质点非稳定平衡位置。

【题2】求出厚透镜对两个不同波长有同一焦距的条件，并就不同类型的透镜讨论可行性。

解答：我们必须知道厚透镜的性质。

国际物理竞赛试题及答案一、选择题（每题5分，共20分）1. 光在真空中的传播速度是：A. 299,792,458 m/sB. 299,792,458 km/sC. 299,792,458 cm/sD. 299,792,458 mm/s答案：A2. 根据牛顿第三定律，作用力和反作用力：A. 总是相等的B. 总是相反的C. 总是同时出现的D. 总是同时消失的答案：A3. 以下哪种物质的密度不是1 g/cm³？A. 水B. 酒精C. 汞D. 空气答案：D4. 一个物体在自由落体运动中，其加速度是：A. 9.8 m/s²B. 10 m/s²C. 11 m/s²D. 12 m/s²答案：A二、填空题（每题5分，共20分）1. 根据热力学第一定律，能量守恒的数学表达式是：__________。

答案：ΔU = Q - W2. 电磁波谱中，波长最长的是__________。

答案：无线电波3. 欧姆定律的公式是：__________。

答案：V = IR4. 根据狭义相对论，当物体的速度接近光速时，其质量会增加，这种现象称为__________。

答案：相对论性质量增加三、计算题（每题10分，共30分）1. 一个质量为2kg的物体，从静止开始以2 m/s²的加速度下落，求物体下落10秒后的速度和位移。

答案：速度 v = at = 2 m/s² × 10 s = 20 m/s位移s = 0.5 × a × t² = 0.5 × 2 m/s² × (10 s)² = 100 m2. 一个电阻为10Ω的电阻器通过电流2A，求电阻器两端的电压。

答案：电压V = IR = 10Ω × 2A = 20V3. 一个物体从高度h自由落下，不考虑空气阻力，求物体下落时间t。

答案：t = √(2h/g)，其中g为重力加速度，取9.8 m/s²。

历届国际物理奥林匹克竞赛试题与解答第６届（1972年于罗马尼亚的布加勒斯特）【题１】给定三个圆柱，它们的长度、外径和质量均相同。

第一个是实心圆柱；第二个是空心圆筒，壁有一定厚度；第三个是同样壁厚的圆筒，但两端用薄片封闭，里面充满一种密度与筒壁相同的液体。

如将它们放在倾角α为的斜面上，如图6.1所示，求出并比较这些圆柱的线加速度。

研究光滑滚动与又滚又滑两种情况。

圆柱与斜面的摩擦系数为μ，液体与筒壁之间的摩擦可以忽略。

解：沿斜面方向作用在圆柱上的力是：作用于质心重力的分量mg sin 和作用于接触点的摩擦力S ，如图6.1所示。

产生的加速度a ：ma ＝mg sin －S 纯滚动时的角加速度为： R a ＝β 转动的运动方程为： I Ra RS = 以上方程组的解为： 21sin mR I g a +=α221sin mR I mR Img S +⋅=α （１）当S 达到最大可能值μmg cos 时，也就到了纯滚动的极限情形，这时：221sin cos mR I mR I mg mg h h +=ααμ即维持纯滚动的极限条件为)1(tan 2ImR h +=μα （２） 下面我们来研究三个圆柱体的纯滚动情形。

（Ⅰ）实心圆柱的转动惯量为221mR I =从（１）式和（２）式分别得到 αsin 32g a =， tan a h ＝３μ ααmg sin S R角加速度为：β＝Ra （Ⅱ）设空心圆筒壁的密度是实心圆柱密度的n 倍。

因已知圆柱的质量是相等的，故可以算出圆筒空腔的半径r ：)(222r R L n L R -=ρπρπ 即nn R r 122-= 转动惯量为：nn mR r LR n R LR n I 125.05.05.022222-=⋅-⋅=ρπρπ 由（１）式和（２）式分别算出： αsin 142g n n a -=， μα1214tan --=n n h 角加速度为：β＝Ra （Ⅲ）对充满液体的圆筒，因液体与筒壁之间无摩擦力，故液体不转动。