运动学，速度，和向量基础

• These notes cover basic physics concepts, including kinematics, vectors, motion, and forces.

Formula Symbols

• v = 速度 (velocity)
• t = 时间 (time)
• a = 加速度 (acceleration)
• d = 距离 (distance)

SUVAT

• SUVAT is an acronym used in kinematics to represent:
  • s = 位移/距离 (displacement/distance)
  • t = 时间 (time)
  • a = 加速度 (acceleration)
  • u = 初速度 (initial velocity)
  • v = 末速度 (final velocity)
• "Initial" refers to data at the beginning of a scenario.

运动学 (Kinematics)

• 描述物体运动的物理学分支 (Physics that deals with the description of motion)
• 速度 (Speed): indicates how fast an object is moving, typically measured in 米/秒 (m/s)
• 速率 (Velocity): Speed in a specific direction, also measured in 米/秒 (m/s), considered a 向量 (vector)
• 曲线速度 (Curve Velocity)：通过曲线形状计算面积和距离 (calculating area and distance using the shape of a curve)
• 位移 (Displacement): The change in position with magnitude, also a 向量 (vector)

向量 (Vectors)

• 单位含有方向和大小 (Units with both direction and magnitude)

公制系统 (Metric System)

• 基于基本单位的变化 (Change of Length in different space)
  • 基本单位包括 米 (m), 克 (g), 升 (litres), 秒 (seconds), 牛顿 (Newtons (N)), m, g, l, and sec. are fundamental units
  • 牛顿 (Newtons) 不是基本单位 (not a fundamental unit).
• 从大到小 (From Bigger to Smaller): giga(G), mega(M), kilo(k), hecto(h), deca(d), base(mid), deci(d), centi(c), milli(m), micro, nano(n)
• These terms are of Greek origin.
• 单位可转换为米制 (Units can be converted, representing values in meters)
  • Ex: 24000 cm = 0.00024 Mm

视差 (Parallax)

• 从不同角度观察物体时位置的偏移 (Shift in object position when viewed from different angles)

物理与数学 (Physics and Math)

• They are related through 方程 (equations)

线性关系 (Linear Relationship)

• 物理图像呈直线 (Physics graph is a straight line)
  • 正比关系 (Direct Relationship): x and y 轴 (axis), starts from zero
  • 反比关系 (In direct): lines are not from 0 0
• 斜率公式 (Equation form of slope):
  • 用于线性关系 (used for a linear graph) -y=mx+b, where m = slope and y = dependent variable
• 斜率查找(How to find slope): 升/跑 (rise/run)

匀速 (Uniform Speed)

• 公式是 v=s/t (formula v=s/t).

反比关系 (Inverse Relationship)

• 可以是 xy=k 或 y = k/x (equation that can be xy=k or y = k/X)
  • 可以改变方程的变量 (you can adjust the variables of the the equation)
  • 有些变量不能改变 (some variables cannot change)
• 图形包含曲线 (graphs use curve lines)
  • 曲线不会接触graph上的任何点 (the line won't touch any point on the graph)

三角符号 (Triangle Symbol)

• 表示变量的变化 (Indicates change in that symbol)
  • 时间变化 (change of time) or 速度变化 (change of speed).)

二次 (Quadratic)

• Form: y=kx^2
• 图形以点开始，然后弯曲 (Graphs start at a point and then curve)

描述运动 (Describing Motion)

• 通过图像、数据表格和公式进行说明 (Illustrate with graphs, data tables, and equations)
• Write a conclusion sentence.

单位转换 (Unit Conversions)

• 1000 m = 1 km
• 100 cm = 1 m
• 100000 cm = 1 km
• If converting to a higher metric, divide by 1000, 100, or 100000.
• If converting to a lower metric, multiply by 1000, 100, or 100000.

标量和向量 (Scalars and Vectors)

• 标量 (Scalar): only has magnitude.
• 向量 (Vectors): magnitude and direction.
• 向量 (Vectors)方向不同于标量 (scalars), vectors have a direction.
• 标量和向量的符号相同，向量符号上方有箭头 (symbols are the same, but vectors have an arrow).

相对运动 (Relative Motion)

• 物体相对于另一个物体的运动 (Motion of one object relative to another)
• if it is the first object, the motion is Formula: (u-v)m/s -If it's the second object moving in the opposite direction is, Formula: (u+v)m/s, if people is looking the velocity is 0.

平均速度 (Average Velocity)

• 公式 (Formula): 位移变化/时间变化 (change in distance/change in time)
  • 用于计算平均速度 (used to find average change)
• 恒定速度意味着数据具有恒定的速度 (Same average velocity means constant velocity)
• 速度变化率 (rate of change in an objects position)
• 简化版：Vave (Simplified version: Vave)

斜率符号 (Different Symbols for Slope)

• 上坡 +(Uphill slope: +)
• 下坡 -(Downhill slope: -)
• 没有变化的斜坡 0 (No Change: 0)
• 不移动 (if not moving)

位置（位移）时间图 (Position (Displacement) Time Graph)

• 显示速度 (shows the speed)
  • 比较两个物体的相交点，显示距离和时间之间的关系
  • (Compare intersect points of 2 objects, shows relationship between distance and time)
  • 数据可用于计算平均速度 (data can calculate average velocity.)
• 比较两个对象 (Compare 2 objects): 线可以是线性或曲线 (lines can be linear or curved).
  • 内插值可能包含小数 (interpolation can contains decimals).
• 简化距离-时间图 (simplified d-t graph.)
• 斜率是物体的速度 (slope is the velocity of an object).
• 可以使用数据表显示 (can be shown with a data table.)

速度-时间图 (Velocity-Time Graph)

• 显示速度和时间之间的关系 (shows the relationship between speed and time.)
• 速度时间图的斜率 (Slope of velocity-time graph:)
  • 斜率=加速度 (slope = acceleration.)
    • Formual= acceleration is a times change of time = final velocity - inital velocity.
  • 公式可以转化为 (formula can be converted. to:) a= change in velocity / change of time
    • 加速度=速度变化/时间变化 (accelaration = change in velocity / change in time.) -时间变化=最终时间-初始时间 (Change of time = final time - initial time) -加速 (Accelerate.)

速度时间图的面积 (Area of the v-t graph:)

• 面积 (area) = 物体移动的距离 (Distance Travel by the object.)
• 距离=时间变化 *（最终速度+初始速度）/2 (d= change in time (vf+vi)/2) -时间变化=最终时间-初始时间 (change in time= time final - time initial.)
• 速度变化=最终速度-初始速度 (change in velocity= velocity final- velocity initial.)

加速度和距离 (Acceleration and Distance Traveled)

• 当寻找加速度和距离时 (When you are finding acceleration and distance.)
  • d= 初始速度*时间变化+（加速度（时间变化^2)）/ 2 (d= velocity initial times change in time +(acceleration times ( change in time)^2)/2)
  • 初始速度=原始速度 (Velocity initial= original velocity)
  • 距离 (Distantion)

加速度和时间 (Acceleration and Time Traveled)

• 当寻找时间和加速度时 (When finding the time and acceleration.)
• 2ad = （最终速度)^2（-初始速度)^2((v final)^2 - (V initial)^2)
• 加速度 = 速度变化/时间变化 (a= acceleration = change in velocity/ change in time)
• 距离 (Distantion)

初始速度 (Velocity Initial)

• 距离=（最终速度*时间变化）- （加速度（时间变化)^2)/2 (distance= (velocity final times change of time)- (a(change of time)^2)/2)
• 加速度 = 速度变化/时间变化 (a = acceleration= change of velocity/ change of time)
• 距离 (Distantion)

最终速度 (Final Velocity)

• at+initial velocity

加速度 (Acceleration)

• 速度变化（速度和位置）(The change of velocity ( speed and location ))
  • 公式 (Formula:)
    • 加速度=速度变化/时间 (a= change in velocity / time), 可以变成: 加速度*时间=速度变化(which can be: a x time= change in velocity.)

自由落体物体 (Free Falling Object)

• 由于重力，加速度会发生 (Acceleration happens due to gravity.)
  • 近地重力：9.81 m/s^2 (Near earth: 9.81 m/s^2)
• 用于自由落体的5个加速度公式 (5 acceleration formulas for free-falling):
  • 重力 (gravity:)g=速度变化/时间 (g= change in velocity/ change in time.)

抛掷运动 (Tossed Motion)

• 不等于零 (not equal to zero)
• 向上运动的时间应该与向下运动的时间相同 (the time of going up should be the same as the time going down)
  • 减速 (Deceleration): -9.81m/s^2
    • 上升：v=0 (Going up: v=0)
  • 加速 (Acceleration): 9.81, 落下：u=0 (going down:) if a objec fly above and try to fight gravity the energy will be -9.81 m/s^2, the objec will decelerate. Velocity become O or get into minus -当球到达最高点时，速度=0 (When the ball arrives at the top point, the velocity=0)

抛体运动 (Projectile Motion)

• 水平抛体 (Horizontal projectile:)
  • 从物体上掉落的两个物体会水平移动 (two things drop from a object that will move horizontally.)
  • 通过移动物体的抛射物会撞击地面 (the projectile gets strike to the ground by the object that moves horizontally.)
  • 同时掉落和击中 (drop and hit at the same time.) -由于相同的重力和相同的时间，下降所需的时间也相同 (due to same gravity and same time, same time taking to drop) -物体的速度在水平方向上是不变的，除非受到外力作用 (an object's speed will be constant when going horizontally unless external force.)
  • 重力是其中之一 (Gravity is one of it)

加速 (Acceleration:)

• 速度的变化和位置/大小 (The change of speed and it's position/magnitude.
• a=速度变化/时间 (a=change in velocity/time taken)

力 (Forces)

• 动力学 (Dynamics:):
  • 研究运动发生的原因 (study of why motion occurs)
• 牛顿运动定律 (Newton's Law of Motion:)
  • 艾萨克·牛顿 (Issac Newton)
    • 研究力和物体之间的相互作用 (Study of interactions between forces and objects)
      • 四种主要类型力 (The 4 major types (4 forces)):
  • 重力 (gravitational forces:) 最弱的 (weakest of all.) 可以观察和看到 (you can observe and see it.)
  • 重力=9.81-下落 (gravity a = 9.81- falling)
  • 例如：岩石落到地球上 (example:)
  • 电磁力 (Electromagnetic forces):
  • 磁铁 (magnets)
  • 铁和磁铁可以粘在一起 (iron and magnet can stick together)
  • 强核力 (strong nuclear forces:)
    • 将粒子保持在一起的力 (force that hold particles together.)
      • 在原子核中 (in the nucleus)
  • 弱核力 (weak nuclear forces:) - 原子核的自然衰变 (natural decay of an nucleus in an atom.) - 逃逸粒子的较弱力 (weaker force that particle escapes.)
• 能量 (Energy:) -vector with magnitude and direction
  • Vectors

惯性 (Inertia:)

• 物体的性质，以恒定的速度静止或移动，而不受任何影响 (nature of objects that rest or move at a constant speed.)
  • 没有其他力的作用下，物体将以恒定的速度移动 (without any other force, an object will move at a constant speed.)
  • 如果没有任何影响，物体将保持静止 (object will remain rest if nothing is affecting it.)
  • 质量越大，惯性越高 (the greater the mass, the higher the inertia is.)

牛顿三大运动定律 (Newton's 3 Laws of Motion:)

• 一维运动定律 (1st Law:) 法则
  • 惯性定律 (law of inertia.)
    • 如果力平衡，所有物体保持静止或以恒定速度移动 (object will remain at rest or move at constance spedd if the force is balance.)
    • 如果力不平衡，力可能会加速 ( the force might accelerate if the force is unbalance.)
• 二维运动定律 (2nd Law:)
• 力=质量*加速度 (F=ma)
  • 力=净力 (F= net force.)
    • 以牛顿为单位计算 (calculated in newtons)
  • 质量=m (m=mass)
    • 有多重 ( how heavy it is,) 按千克测量 (measured by kg)
  • 加速度是物体的加速度 ( a= acceleration of the object.)
  • 加速度应与净力成正比 (acceleration should be propertional to net fore.)
• 3rd Law of Motion
  • Action-reaction law An equal and oppostite force to every action force.
    • 力会反弹回本身 (the force will bounce back to yourself)
      • 或者，反弹回另一种类型的力量 (or bounce back to another type of force.)
      • 例如：当你击打石头时，你的手会受到很大的痛苦 (ex: when you hit a stone, your hand will suffer in great pain.)

2 dimensional motions

• 通过图形计算向量 (Solving vectors graphically:)
  • 标量 (scalars:) 物理量仅按大小描述 (physical quantities only described by magnitude.)
  • 向量 (vector:) 按大小和方向描述的物理量，位置箭头 (physical quantities that describe by both magnitude and direction: position arrow.)
    • 显示方向 (shows the direction)
    • 与算术加法不相等 (does not equal arithmic addition.)
      • 总和 (Sum)
        • 排除一个维度 (one dimension is excluded.)
          • 当问题假设方向时，就会发生这种情况 (if the question is assume direcitons)

计算向量

• 计算时 (When calcuating:) 可以按照任何顺序完成 (can be done in every orders)
• 它们可以使用角度 (they can be used in angles:) -Straight north is 90 degree'
  • 35 degree west of south is 235 degrees

###For Postion: Position arrows can be used

• 显示方向和大小 (shows the direction and magnitude:) -where there're heads and tails - Heads always displays the position to the back - Tails show Position (east, south, west, north)

如果距离的位置包括东西方 (if position includes west or east:)

• 使用勾股定理计算 (calculate it the Pythagorean theorem)
• 您还需要包含距离和执行动作的角度。 (Need to include both angle and distance of what's being excuted) -您只需要对南北或东西进行减法或抽象。(just need to do subtraction or abstraction for north or south or west and east)
• 例子：一个男孩向北走3公里，然后向南走2.5公里。他的位移是多少？( Example: A boy walks 3 km north then 2.5km south. What's his displacement?)
  • 3 3-2.5=0.5 north
  • 答案也是肯定的 (the anwser is possitive.)

向量问题 (Vector problems)

• 向量分量相加 (Vector quantities addition:)
  • adding xy.
• Beaning
  • 使用勾股定理求总距离 (use Pythagorean theorem to find the total distance)
  • 然后使用三角函数来求角度 (use trigonometry to find the angles.)
  • 如果是非直角三角形，就用余弦和正弦的乘积 (use cosine and sine law when its a nonright triangle) -物体抛射时的启动角度 (Object Launched at an Angle:)

速度-时间问题 (Velocity-Time Problems)

• 当船移动时，从船底到船的不同部分的时间是相同的 (When a boat is moving, time of going from the base to different parts of the boat is the same.)
  • 对于某些部分而言并非如此 (Not for some of its part:)
    • 仍然是匀速运动 (Still Constant Motion.)
    • 角度发生变化时可以改变方向 (can change direction when the angle is changed)
    • 可以通过2个方向分量启动 (can be launched by 2 direction component:) -垂直运动 (vertical motion) - 通过重力 (by gravity)
• 水平运动 (horizontl motion.)
• 初始速度 (inital velocity)
• 上升角度 (Upward Angles.)
  • 使用勾股定理计算或者三角函数 (use the Pythagorean theorem)