Раздел 4: Дальнейшая механика, поля и частицы
Pearson Edexcel · International A-Level · Physics Тема 4 28:57 Английское озвучивание · Английский + китайские субтитры (встроенные)
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A car bumper changes a momentum transfer by changing the stopping time. A detector uses curved tracks to infer momentum.
汽车保险杠通过改变停止时间来改变力的大小，探测器则通过弯曲轨迹推断动量。
We will connect those ideas through circular motion, fields, capacitors and particles.
本课把碰撞、圆周运动、场、电容器和粒子联系起来。
Keep directions, units and assumptions beside each equation.
每个方程都要配合方向、单位和适用条件。
This lesson is a route through the full reference; use the corresponding skill sheet before each authentic question set.
先完成相应的技能练习，再做真实试题。
Momentum is a vector.
动量是矢量。
If a ball rebounds, its final velocity has the opposite sign to its initial velocity.
小球反弹后，末速度与初速度符号相反。
Subtract initial momentum from final momentum before dividing by contact time.
先用末动量减初动量，再除以接触时间。
Increasing stopping time reduces average force only when the momentum change is the same.
只有动量变化相同时，延长停止时间才会减小平均力。
The wall experiences the opposite force, but that is a force on a different object.
墙受到的反作用力作用在另一个物体上。
The negative triangular area is minus two newton seconds.
负三角形面积为负二牛顿秒。
Dividing by the full contact time gives minus forty newtons as average force, although the peak reaches minus eighty.
除以整个接触时间得到负四十牛顿的平均力，而峰值为负八十牛顿。
Area, maximum height and average height are different quantities. Read the force axis and its sign before calculating.
面积、最大高度和平均高度是不同的量，计算前先读清力轴及其正负方向。
Choose the approach direction as positive.
取接近墙的方向为正。
Write the change in momentum with the signed final velocity. Then divide by contact time.
把带符号的末速度代入动量变化，再除以接触时间。
Give the direction as well as the number.
除数值外还要说明方向。
Pause and attempt both results before the next frame.
暂停并先独立完成两个结果。
The velocity change is minus eight metres per second, not minus two.
速度变化为负八米每秒，不是负二。
Multiplying by zero point three kilograms gives minus two point four newton seconds. Divide that impulse by zero point zero four seconds to obtain minus sixty newtons.
乘以零点三千克得到负二点四牛顿秒，再除以零点零四秒得到负六十牛顿。
Both signs indicate a direction opposite to the approach.
两个负号都表示方向与接近墙的方向相反。
For an isolated system, total momentum is conserved in each perpendicular direction.
孤立系统在两个相互垂直方向上的总动量分别守恒。
In this symmetric example the transverse components cancel. The forward components must add to the incoming momentum, which determines the angle.
在这个对称例子中，横向分量相互抵消，沿原运动方向的分量之和等于入射动量，由此求出角度。
Test kinetic energy separately: momentum conservation alone does not establish an elastic collision.
还必须单独比较动能，动量守恒不能证明碰撞是弹性的。
An elastic collision conserves total kinetic energy as well as momentum.
弹性碰撞同时保持总动量和总动能。
Deriving kinetic energy in terms of momentum shows why equal energy does not mean equal momentum.
把动能改写成动量与质量的关系，就能看出等动能不代表等动量。
In core practical nine, zero the force sensor and resolve the whole pulse with fast sampling. In core practical ten, calibrate distances and frame times, track both velocity components and compare with uncertainty.
核心实验九要调零并用足够高的采样率记录完整力脉冲；实验十要校准长度和帧时间，测量两个速度分量，并结合不确定度比较结果。
Keep trolleys and spheres contained.
注意防止小车和小球掉落。
In core practical nine, secure a trolley track and zero the force sensor.
核心实验九要固定小车轨道并把力传感器调零。
A fast data logger must capture the whole contact pulse.
采样必须足够快，记录完整的碰撞脉冲。
Use light gates or a motion sensor to measure velocities just before and after contact independently.
用光电门或运动传感器独立测量碰撞前后的带符号速度。
Integrate the force-time area and compare it with mass times the signed velocity change.
比较力与时间图像面积和质量乘速度变化。
Repeating trials tests consistency. Friction, offsets and missed pulse tails can explain a mismatch; do not change the data to force agreement.
重复实验检查一致性；摩擦、零点偏移和遗漏的脉冲尾部可能导致差异，不能为使结果相同而修改数据。
For core practical ten, use a level surface and an overhead camera perpendicular to the collision plane. Place a length scale in that same plane and know the frame rate.
核心实验十使用水平表面和垂直拍摄的俯视相机，把长度标尺放在碰撞平面内，并记录帧率。
Track each sphere centre over several frames before and after impact. Convert pixel displacement and frame intervals into velocity components.
在碰撞前后各追踪数帧球心位置，把像素位移和帧间隔转换为速度分量。
Compare momentum in each axis, then kinetic energy separately.
分别比较两个方向的总动量，再比较总动能。
Repeat different collisions, assess position, timing and scale uncertainties, and contain the spheres.
重复不同碰撞，考虑位置、时间和标定不确定度，并防止小球滚落。
A small difference within uncertainty does not demonstrate failure of conservation.
不确定度范围内的小差异不能证明守恒定律失效。
One radian corresponds to an arc equal to the radius.
一弧度对应的弧长等于半径。
Convert revolutions per minute to revolutions per second before multiplying by two pi.
先把每分钟转数换成每秒转数，再乘二π。
Keep the unrounded angular speed for later steps.
后续计算保留未舍入的角速度。
Points on one rigid disc have the same angular speed, but tangential speed increases with radius.
同一刚性圆盘各点角速度相同，但切向速率随半径增大。
Convert degrees to radians before using arc-length or circular-motion equations.
使用弧长或圆周运动方程前，先把角度转为弧度。
Angular velocity measures the rate of angular displacement; use a consistent sign convention for rotation.
角速度表示角位移的变化率，旋转方向要使用一致的正负约定。
All points on a rigid turntable turn through the same angle in the same time. Their angular speeds match, but tangential speed increases with radius and its direction is tangent at each position.
刚性转盘上各点在同一时间转过相同角度，因此角速率相同，但切向速率随半径增加，速度方向在各位置都沿切线。
Doubling radius does not double angular speed.
半径加倍并不使角速度加倍。
Subtract the initial velocity vector from the final vector.
用末速度矢量减初速度矢量。
For a small angular change, the velocity triangle is similar to the radius triangle.
转角很小时，速度三角形与半径三角形相似。
The velocity change divided by speed equals arc displacement divided by radius in the limit. Divide by the time interval to obtain speed squared over radius.
在极限情况下，速度变化与速率之比等于弧长变化与半径之比，再除以时间间隔便得到速率平方除以半径。
Constant speed still permits acceleration because direction changes.
方向变化意味着速度变化，所以速率不变仍然可以有加速度。
Do not add an extra centripetal arrow to the real forces.
不要在真实受力图上再加一个向心力箭头。
At the bottom, reaction minus weight provides the inward resultant. At the top, reaction plus weight provides it.
在底部，支持力减重力提供向内合力；在顶部，支持力加重力提供向内合力。
For equal speed and radius the required resultant is the same, but the reaction differs.
速率和半径相同时，所需合力相同，但支持力不同。
A surface can push; it cannot provide a pulling normal reaction after contact is lost.
失去接触后，表面不能提供拉力式的法向作用力。
Choose inward as the positive radial direction separately at each position.
在每个位置分别取指向圆心为径向正方向。
At the bottom of a rotating drum, the normal force points up and weight points down, so subtract weight. At the top, both forces point down towards the centre, so add them.
圆筒底部支持力向上、重力向下，所以相减；顶部两个力均向下指向圆心，所以相加。
These are equations for actual forces on the same object.
这些都是同一物体所受的真实力。
A surface can push but cannot supply a negative normal force; such a result signals loss of contact.
表面只能推，算出负支持力说明保持接触的假设失效。
After release the initial velocity is tangent, with subsequent motion determined by remaining forces.
释放瞬间速度沿切线，随后运动由剩余的力决定。
Friction is the actual force supplying the inward resultant.
摩擦力是提供向内合力的真实作用力。
Write the required force at radius r and compare it with the largest friction allowed by the stem.
写出半径为r时所需的力，再与题目给出的最大摩擦力比较。
Rearrange before substituting. Check which quantities cancel and explain why.
先变形再代数值，并说明哪些量相消以及原因。
The largest radius is about zero point one two three metres.
最大半径约为零点一二三米。
Doubling mass doubles both the required force and the available limiting friction, so this radius stays unchanged under the stated model.
质量加倍会同时使所需合力和最大摩擦力加倍，因此在给定模型下，半径不变。
If the inward constraint disappears, velocity is initially tangent. Gravity can bend the later path.
向内约束消失时，初速度方向沿切线，重力随后可能使轨迹弯曲。
Electric field strength is force per unit positive test charge and has direction.
电场强度是单位正试探电荷受到的力，是矢量。
Potential is potential energy per charge and is a signed scalar relative to a reference.
电势是相对于参考位置的单位电荷电势能，是带符号的标量。
For a positive charge moving to lower potential, potential energy decreases and the field does positive work. A negative charge feels force opposite to the field.
正电荷移向低电势时，电势能减小，电场做正功；负电荷所受力方向与电场相反。
For a positive source, radial field lines point outwards. The dashed equipotentials cross them at right angles.
正点电荷的电场线向外，虚线等势面与电场线正交。
Between parallel plates, field points from higher to lower potential.
平行板间的电场从高电势指向低电势。
A movement along an equipotential changes no electric potential energy.
沿等势面移动不会改变电势能。
These lines represent different quantities; do not use potential as a vector.
两种线表示不同的物理量，不要把电势当作矢量。
The potential is given at the sphere surface, so use the sphere radius to find its charge.
已知的是球面电势，因此用球半径求电荷。
The requested field is at a different distance from the centre. Use that new distance in the squared denominator. The field is outward for positive charge.
要求的场强对应另一个距球心的距离，平方分母中应使用这个新距离。
Confusing surface radius and observation distance changes the physical question.
正电荷的场向外。 混淆球半径和观察点距离，就会算错物理情景。
For a positive point charge, potential at r is the area under the radial field graph from r to infinity. It is not the area from zero to r.
正点电荷在r处的电势，等于径向场强图从r到无穷远下方的面积，不是从零到r的面积。
Field is related to the potential gradient, so a zero potential value need not imply zero field.
场强与电势梯度有关，所以电势为零不一定表示场强为零。
Equally spaced potential levels packed more closely together correspond to stronger field.
相同电势间隔对应的等势面越密集，场越强。
Use force balance, but decide the charge sign from the required electrical force direction.
用受力平衡计算，但先根据电场力所需方向判断电荷正负。
Gravity is downwards, so electrical force must be upwards.
重力向下，电场力必须向上。
Then use the magnitude equation and divide by the elementary charge.
然后用力的大小关系求电荷量，再除以元电荷。
Pause before seeing the result.
先暂停独立计算。
A downward field exerts upward force on a negative charge, so this drop has two excess electrons.
电场向下时，负电荷受到向上的力，所以油滴多了两个电子。
For a grain specified by density and diameter, first use sphere volume to find mass.
若尘粒给出密度和直径，先用球体积求质量。
The lift threshold compares electrical force with weight; on a tilted panel the normal component of weight is mass g cosine theta, with adhesion excluded in this model.
起飞阈值比较电场力与重力；倾斜面上的法向重力为mg乘余弦，但这里的模型忽略黏附力。
For a spherical dust grain, mass comes from density times volume, so it depends on radius cubed.
球形尘粒的质量等于密度乘体积，因此与半径三次方成正比。
Equate electric lift to the appropriate weight component to obtain a limiting radius, then double it if the options give diameter.
把电场力与相应的重力分量相等，求出极限半径；若选项给直径，需要乘二。
If the field is normal to a tilted panel, compare the electric force with weight normal to that panel, not the whole weight. A separate downslope component remains.
电场垂直斜面时，应比较重力的法向分量，而不是整个重力，沿斜面向下的分量仍然存在。
A threshold is a boundary; choose a permitted size below it, not the nearest size above.
极限值是边界，应选低于边界的最大可选尺寸。
The capacitor plates carry equal and opposite charges in the ideal model. The quoted Q is the magnitude on either plate.
理想电容器两极板带等量异号电荷，Q是任一极板上的电荷量大小。
Plotting voltage against charge gives gradient one over capacitance. The area is work done charging, and the triangular area produces the factor one half.
电压对电荷图的斜率为电容的倒数，图下面积给出充电做功，三角形面积产生二分之一因子。
When discharging between nonzero voltages, subtract squared voltages; do not square the voltage difference.
两个非零电压之间放电时，要相减电压平方，而不是把电压差平方。
Charging capacitor voltage rises towards the supply. Charging current falls because the resistor voltage falls.
充电时电容器电压逐渐接近电源电压，电阻电压和电流则下降。
In discharge, voltage, charge and current magnitude all fall exponentially.
放电时电压、电荷量和电流大小都按指数规律减小。
After one time constant they are one over e of their starting values.
一个时间常数后为初值的e分之一。
The log graph has slope minus one only because its time axis here is divided by RC; against seconds the slope is minus one over RC.
图中的对数斜率为负一，是因为横轴为t除以RC；若横轴为秒，斜率就是负一除以RC。
First calculate the time constant in seconds. Then use the exponential voltage relation at three seconds.
先把时间常数算成秒，再用指数电压公式求三秒后的电压。
Finally subtract final stored energy from initial stored energy.
最后用初始储能减末储能。
Write the symbolic equation for each stage before the numbers.
每一步都先写符号方程，再代数值。
The time constant is two seconds, so three seconds is one and a half time constants.
时间常数为两秒，因此三秒相当于一个半时间常数。
Voltage is about two point six eight volts. Energy lost is about six point eight four millijoules and becomes mainly heat in the resistor.
电压约为二点六八伏，损失的储能约为六点八四毫焦，主要成为电阻中的热。
Energy does not follow the same fractional decay as voltage because stored energy depends on voltage squared.
储能与电压平方有关，所以储能的衰减比例与电压不同。
The switch selects charging from the supply or discharging through the same resistor. The sensor is connected across the capacitor.
开关选择从电源充电或通过同一电阻放电，传感器并联在电容器两端。
Choose a sampling interval short compared with RC and a sensor input resistance much larger than the discharge resistance.
采样间隔应远小于RC，传感器输入电阻应远大于放电电阻。
Charge to the same initial voltage for repeats.
重复实验前恢复相同初始电压。
Observe capacitor polarity and voltage rating, then discharge through a resistor before changing connections.
注意电容器极性和额定电压，改接电路前通过电阻安全放电。
A log fit can estimate RC from several readings.
用多个读数的对数拟合可求RC。
Two voltages from one uninterrupted discharge give a resistance when capacitance is known.
已知电容时，同一次连续放电的两个电压可用于求电阻。
Compare that resistance with the full permitted interval, and consider capacitance uncertainty if it is not stipulated exact.
要与整个允许区间比较；除非题目规定电容精确，否则还要考虑其不确定度。
Smaller load resistance makes smoothing worse because the capacitor discharges faster between supply peaks.
负载电阻减小会加快峰值之间的放电，使滤波变差。
Identical series capacitors share voltage and carry the same charge magnitude.
相同串联电容器平分电压，电荷量大小相同。
A smoothing capacitor recharges near each supply peak and supplies the load between peaks.
平滑电容器在电源峰值附近重新充电，在峰值之间向负载放电。
A lower load resistance gives faster discharge and poorer smoothing.
负载电阻越小，放电越快，平滑效果越差。
In a series pair of identical capacitors, the same charge magnitude appears on each and each takes half the supply voltage. Relative to one identical capacitor connected alone, each then stores half the charge.
两个相同电容器串联时，各自电荷量相同、各分得一半电源电压，因此每个的电荷量是单独接同样电源时的一半。
In core practical eleven, keep the components fixed and restore the same initial charge before repeating. Leakage and voltmeter input resistance affect the effective discharge path; readings near zero have large relative uncertainty.
核心实验十一应保持元件不变，每次恢复同样的初始电荷；漏电和电压表输入电阻会改变有效放电通路，接近零的电压读数相对不确定度很大。
For force, use the angle between current or particle velocity and the magnetic field. For magnetic flux, use the angle between field and the area normal.
磁力公式中的角是电流或粒子速度与磁场之间的角，磁通量公式中的角是磁场与面积法线之间的角。
The left-hand rule uses conventional current; reverse the force for an electron moving in the stated direction.
左手定则使用约定电流方向；电子运动时要把力的方向反转。
A perpendicular magnetic force changes direction without doing work.
与速度垂直的磁力改变方向，但不做功。
The field is perpendicular to the coil plane, so it is parallel to the normal and the cosine factor is one.
磁场垂直线圈平面，也就是平行于法线，所以余弦因子为一。
Use radius squared to calculate area. Multiply flux by forty turns to obtain linkage.
用半径平方求面积，再乘四十匝得到磁通链。
A balance measures the reaction on the magnets when the wire is supported separately; convert its mass-reading change into a force using g.
若导线独立支撑，天平测到的是磁体受到的反作用力，应把质量示值变化乘g换成力。
Draw separate force diagrams for the wire and the magnets.
应分别画导线和磁体的受力图。
A balance under magnets does not directly measure the force on a separately supported wire. It measures the magnets’ reaction, equal in magnitude and opposite in direction.
磁体下的天平并不直接测量独立支架上的导线受力，而是测量磁体受到的反作用力，其大小相等、方向相反。
Convert a mass reading change into force by multiplying by gravitational field strength. Then use the active wire length and the perpendicular field component.
把天平质量读数的变化乘以重力场强，才得到力；再使用有效导线长度和垂直磁场分量。
Do not substitute the balance mass directly into the magnetic-force equation.
不能把质量读数直接代入磁力方程。
The two flux values share the factor ten to the minus five.
两个磁通量数值都乘十的负五次方。
Find the change per turn, multiply by turn count and divide by the interval.
先求每匝磁通变化，再乘匝数并除以时间。
For direction, ask whether the original linked field is increasing or decreasing. Do not merely say that induction opposes the field.
判断方向时要区分原磁通量是增加还是减少，不要笼统地说感应效应总与原磁场相反。
The average induced e.m.f. is zero point one zero volts.
平均感应电动势为零点一零伏。
Lenz law opposes the change, so a decreasing original flux produces an effect supporting its previous direction.
楞次定律反抗的是变化，所以原磁通量减小时，感应磁场帮助维持原方向。
A field boundary crossing a coil changes area at width times speed, giving N B L v.
磁场边界扫过线圈时，面积变化率为宽度乘速度，因此电动势大小为NBLv。
Reversing pole orientation reverses signal direction.
磁极反向会使信号方向反向。
For a straight field boundary sweeping a rectangular area, speed times boundary width gives area swept per second. Multiply by magnetic flux density and linked turns to obtain the induced electromotive force.
直线磁场边界扫过矩形区域时，速度乘边界宽度等于每秒扫过的面积，再乘磁感应强度和链接匝数，得到感应电动势。
This shortcut requires the specified uniform field and geometry; it is an application of Faraday’s law, not a replacement for it.
这个捷径要求规定的匀强磁场和几何条件，是法拉第定律的应用。 移动更快会提高磁通变化率。
A faster motion increases the rate of flux change. In a magnetic strip reader, reversing pole orientation reverses the signed flux change and signal. Lenz’s law fixes the opposing response.
磁条读卡器中，磁极方向反转会使带符号的磁通变化及信号反向，楞次定律决定反抗变化的响应。
Electromagnetic induction requires changing flux linkage.
电磁感应需要磁通链变化。
A steady direct current after the switching transient does not provide sustained induction.
直流电在接通瞬间之后保持稳定，就不能持续产生感应。
In wireless charging, alternating current changes the transmitter field and the receiver linkage.
无线充电中，交流电使发送线圈的磁场和接收线圈的磁通链不断变化。
Separation and alignment affect how much flux reaches the receiver.
距离和对准情况会影响耦合磁通。
Use this causal chain rather than saying the magnetic field simply transfers electricity.
应解释这条因果链，而不是说磁场直接传送电流。
Most alpha particles pass nearly straight through thin foil, supporting an atom that is mostly empty space.
大多数α粒子几乎直线穿过薄箔，支持原子大部分为空间的结论。
Rare very large deflections require strong electrostatic repulsion concentrated near a tiny positive nucleus. Most mass is concentrated there.
极少数的大角度偏转需要集中在微小正电原子核附近的强静电斥力，原子的质量也主要集中在那里。
A diffuse positive-charge model cannot account for those rare large-angle encounters.
正电荷弥散分布的模型不能解释这些罕见的大角度事件。
In atomic notation, Z counts protons and A counts all nucleons.
原子符号中Z表示质子数，A表示核子总数。
The historical comparison is an evidence argument.
历史模型的比较要依靠证据。
Most alpha particles travel nearly straight through foil. Rare large deflections cannot be explained by a weak positive charge spread throughout the whole atom.
大多数阿尔法粒子几乎直穿金箔，但少数发生大角度偏转，这不能由分布在整个原子中的弱正电荷解释。
A very small, dense, positive nucleus creates a strong repulsive force during a close encounter.
非常小、致密、带正电的原子核在近距离相遇时产生很强的排斥力。
The rarity of such encounters constrains its small size.
相遇稀少说明原子核尺寸很小。
Link each observation to its conclusion; simply naming the nuclear model does not explain the evidence.
每项观察都必须与对应结论联系，不能只写模型名称。
Thermionic emission is release of electrons from a heated metal surface.
热电子发射是加热金属表面释放电子的过程。
A positive electrode accelerates them in vacuum.
正电极在真空中加速电子。
Electric fields change kinetic energy; perpendicular magnetic fields steer.
电场可以改变动能，垂直磁场则改变运动方向。
If the question supplies a de Broglie wavelength, first calculate momentum from h over wavelength, then kinetic energy from momentum squared over twice mass.
若给出德布罗意波长，先用h除以波长求动量，再用动量平方除以二倍质量求动能。
Check that the particle is sufficiently below light speed before using these classical equations.
使用经典方程前，应检查速度是否远低于光速。
A question may give wavelength instead of speed.
题目可能给出波长而不是速度。
Use de Broglie’s equation to find momentum, then the non-relativistic kinetic-energy relation, then divide energy by electron charge magnitude for the accelerating potential difference.
先由德布罗意关系求动量，再由非相对论动能关系求能量，最后除以电子电荷量求加速电压。
This chain assumes the particle starts from rest and remains well below light speed. Otherwise the energy gained is only the change in kinetic energy and the non-relativistic formula may fail.
这条推导要求粒子从静止开始且速度远小于光速，否则电场提供的是动能变化，非相对论公式也可能不适用。
Thermionic emission supplies the electrons; the electric field supplies the acceleration.
热电子发射提供电子，电场负责加速。
A linear accelerator does not accelerate the particle inside an ideal drift tube.
理想漂移管内部不加速粒子。
The tube shields the particle while the alternating voltage reverses. The next gap then has the correct polarity to accelerate again.
粒子在管内时受到屏蔽，同时交变电压反向，使下一个间隙再次加速。
At a fixed frequency the flight time inside successive tubes is kept near a half-period, so tube lengths increase with particle speed.
频率固定时，各管内飞行时间保持在约半个周期，因此粒子越快，管越长。
Count accelerating gaps, not just the tubes drawn.
计算能量时要数加速间隙，不要直接数管子。
The particle gains energy at the gap, then magnetic force bends its path inside a dee without changing speed.
粒子在间隙获得能量，在D形盒内则由磁力弯曲路径，速率不变。
More momentum means a larger radius.
动量越大，半径越大。
The alternating polarity must reverse during each half-turn.
每半周内，间隙电压必须反向。
In the non-relativistic model the half-turn time is independent of speed, which makes fixed-frequency repeated acceleration possible.
在非相对论模型中，半周时间与速率无关，因此能以固定频率反复加速。
This drawing is a schematic path, not a measurement of a particular machine.
这是路径示意图，并非某台加速器的测量图。
Magnetic force supplies the centripetal resultant.
磁力提供向心合力。
Use momentum directly for the radius.
求半径时可以直接使用动量。
For time in one dee, derive the full period first and then halve it.
求一个D形盒内的时间时，先推导完整周期，再取一半。
Pause and check units and the factor of pi before seeing the solution.
暂停计算，并检查单位和π的系数。
The radius is about zero point three one three metres. The time in one dee is about eight point two zero times ten to the minus eight seconds.
半径约为零点三一三米，在一个D形盒内的时间约为八点二零乘十的负八次方秒。
Period depends on mass, charge and field, but not speed in this model.
在此模型中，周期取决于质量、电荷和磁场，而不取决于速率。
Near light speed the classical timing no longer remains valid, and synchronisation with a fixed-frequency field fails.
接近光速时，经典的计时关系失效，固定频率的同步加速受到限制。
A track curves because a force changes momentum direction.
轨迹弯曲说明力改变了动量方向。
To infer charge sign, know both magnetic-field direction and travel direction.
判断电荷正负时，需要同时知道磁场和运动方向。
A missing neutral product may be inferred by subtracting visible momentum vectors; it need not leave a direct ionisation track.
把可见动量矢量相减，可以推断未直接留下电离轨迹的中性产物。
High energy helps resolve small structure through short wavelength and can create new particles.
高能量对应短波长，可分辨细小结构，也能产生新粒子。
Fast muon lifetime increases in the Earth frame without exceeding light speed.
高速μ子的地球参考系平均寿命增大，但速度没有超过光速。
To infer charge sign from a track, combine the field direction with the particle’s direction of travel.
从轨迹判断电荷符号，必须同时知道磁场方向和粒子运动方向。
A circular arc with constant radius cannot itself tell you which way the particle travelled.
半径不变的一段圆弧本身不能确定粒子沿哪个方向运动。
A tightening track often indicates loss of momentum, but interpret it with the detector evidence.
轨迹逐渐收紧通常表示动量减小，但要结合探测器证据。
Fast muons can reach the ground because their mean lifetime in the Earth frame increases near light speed. They do not exceed light speed.
高速缪子能到达地面，是因为接近光速时在地球参考系测得的平均寿命增加，不是因为它们超过光速。
This unit requires understanding that significance, rather than calculating with relativistic equations.
本单元要求理解这一意义，不要求使用相对论公式计算。
A baryon contains three quarks and a meson a quark and antiquark.
重子由三个夸克构成，介子由一个夸克和一个反夸克构成。
A lepton is fundamental in this model; a positron is an antilepton, not a meson.
在此模型中轻子是基本粒子，正电子是反轻子，不是介子。
The proton contains two up quarks and one down quark, giving total charge plus e.
质子含两个上夸克和一个下夸克，总电荷为正e。
The family pattern supported the prediction of the top quark before observation.
夸克家族的规律在实验发现前支持了顶夸克的预测。
Photons are radiation quanta rather than baryons or leptons.
光子是辐射量子，既不是重子也不是轻子。
Add constituent charges rather than memorising an isolated list.
应把组成粒子的电荷相加，而不只是背诵列表。
Two up quarks and one down quark give the proton one positive elementary charge. One up and two down quarks give a neutral neutron.
两个上夸克和一个下夸克使质子带一个正元电荷；一个上夸克和两个下夸克使中子不带净电荷。
Antiquark charges reverse.
反夸克的电荷符号相反。
A baryon has three quarks, whereas a meson has a quark and an antiquark.
重子由三个夸克组成，介子由夸克与反夸克组成。
The family pattern suggested a missing top quark before it was observed: the model generated a testable prediction, not only a way to catalogue known particles.
夸克家族的规律在观测到顶夸克前就预测了它，说明模型能提出可检验的预测。
An electron and positron have equal rest masses and opposite charges. Their lepton numbers are plus one and minus one, while both baryon numbers are zero.
电子和正电子的静质量相同，电荷相反，轻子数分别为正一和负一，而重子数都为零。
A neutral particle can still differ from its antiparticle in another additive quantum number.
中性粒子仍可能与反粒子具有不同的其他可加量子数。
Do not decide particle identity from electric charge alone.
不能只根据电荷判断粒子身份。
Assign each particle its charge, baryon number and lepton number. Add the totals on each side separately.
分别列出各粒子的电荷、重子数和轻子数，再比较等号两边的总和。
Do not assume an equation is valid merely because charge balances.
不能只因电荷守恒，就认为反应式有效。
Pause and identify the symbol change needed to satisfy all three checks.
暂停并找出满足三项检查所需的符号修改。
With an electron neutrino, final lepton number would be plus two rather than zero.
若使用电子中微子，末态轻子数为正二，而不是零。
Replacing it with an electron antineutrino gives plus one minus one, restoring zero. Charge and baryon number already balance.
换成电子反中微子后，正一与负一相加为零，电荷和重子数也守恒。
These are necessary checks, not proof that any proposed reaction occurs: energy, momentum and the actual interaction must also permit it.
这些是必要检查，不能证明任何提出的反应都会发生；还要满足能量、动量及相互作用条件。
Pair production creates a particle and antiparticle from energy, with momentum conserved in the surrounding interaction.
对产生把能量转变为粒子和反粒子，同时整个相互作用必须满足动量守恒。
Electron–positron production needs at least both electron rest energies.
电子与正电子的产生至少需要两份电子静能。
In annihilation of a pair with negligible initial kinetic energy and zero total momentum, two equal-energy photons travel oppositely.
若一对粒子的初始动能可忽略、总动量为零，湮灭产生的两个光子等能、反向运动。
Each carries one electron rest energy; the total carries two.
每个光子具有一份电子静能，总能量为两份。
A single photon cannot alone have zero momentum and nonzero energy.
单个光子不能同时具有非零能量和零动量。
MeV divided by c squared is a mass unit. Multiplying it by c squared gives the corresponding rest energy.
MeV除以c平方是质量单位，乘回c平方才得到对应静能。
Convert electronvolts to joules before dividing by light speed squared to obtain kilograms.
先把电子伏转换为焦耳，再除以光速平方求千克。
For a percentage comparison, identify which accepted mass is the denominator. Keep rest energy, available kinetic energy and total energy distinct.
百分比比较时，要说明分母采用哪个参考质量，并区分静能、可用动能与总能量。
Pause and answer these four checks.
暂停并回答四个检查问题。
At the top of a drum, both the normal contact force and weight point inward while contact remains.
在圆筒顶部，仍保持接触时，支持力与重力都指向圆心。
The log-voltage gradient is minus one over RC.
对数电压与时间图像的斜率等于负的一除以RC。
A magnetic field alone does no work because its force is perpendicular to velocity.
磁力与速度垂直，因此磁场本身不做功。
For a proposed decay, charge conservation is not sufficient: check baryon number, lepton number, energy and momentum.
衰变方程除电荷外，还要检查重子数、轻子数、能量和动量守恒。
Use the reference and the seven paired exercise and authentic sets to repair any gap.
用参考讲义以及七组配套练习和真题修补薄弱点。