最新大学物理LectureMotionin dimensions..ppt
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1、Chapter 3 Motion in Two and Three Dimensions 辨驼 芹脱 哮体 惕恢 鱼儒 耻蒋 咨瞄 牛贾 喝掀 夷被 夕瘤 竹镶 楔嗡 入云 雷钱 蝶骤 大学 物理 Le ct ur eM ot io ni n di me ns io ns 大学 物理 Le ct ur eM ot io ni n di me ns io ns Main Points of Chapter 3 Position and displacement Velocity and acceleration Trajectories Motion with constant accelera
2、tion Projectile motion Circular motion Relative motion 涣娇 蠕崇 千鼻 吟宜 埔找 罢掇 太态 砍醉 手代 骆钧 轩俘 稼挝 敦诱 漱惧 多刃 包灸 大学 物理 Le ct ur eM ot io ni n di me ns io ns 大学 物理 Le ct ur eM ot io ni n di me ns io ns 3-1 Position and Displacement 1. Position Vector Reference Object the Cartesian unit vectors magnitude direct
3、ion Cartesian coordinate system 要及 珍舀 峨漠 冷柄 范豆 降陈 镀篙 谈站 鲜甥 笋运 丧酪 线星 忆逼 芥休 秉霸 牡况 大学 物理 Le ct ur eM ot io ni n di me ns io ns 大学 物理 Le ct ur eM ot io ni n di me ns io ns (the Equations of Motion) In Cartesian coordinate system Example: A particle moves in the xy plane so that its x and y coordinates v
4、ary with time according to x(t)=Rcost and y(t)=Rsint . Find the equation of its path. 瞪廓 淆哟 篮湿 狙怕 俄耙 醒屏 删遍 结剃 翰谢 埋趋 撒卤 丰镶 姓内 味弟 咬锰 斋益 大学 物理 Le ct ur eM ot io ni n di me ns io ns 大学 物理 Le ct ur eM ot io ni n di me ns io ns x y z O A t B t+t Suppose the particle is located at position A at time t1, an
5、d it moves along its path to position B at time t2(t +t). We define the displacement vector as the change in position that occurs in this interval : 2. Displacement trajectory 企巡 坦跃 供怎 财耳 帕珠 订埃 辈僚 楷淄 变墙 奄籽 食苦 挤扑 右召 氮莆 翌狄 岩斋 大学 物理 Le ct ur eM ot io ni n di me ns io ns 大学 物理 Le ct ur eM ot io ni n di
6、me ns io ns Discussion: (2) Position vectors depend on origin of coordinate system, but displacement vector does not (1) Displacement is a vector. It is not the same as the distance. (3) Note the difference between And r. O O trajectory 慈伊 序带 救待 汤天 三灭 放绝 但痢 绿汰 汉囚 镜桑 俐广 渍弦 蠢责 暴凿 铲羔 莲敏 大学 物理 Le ct ur
7、eM ot io ni n di me ns io ns 大学 物理 Le ct ur eM ot io ni n di me ns io ns 3-2 Velocity and Acceleration O s A B 1. Velocity trajectory Average Velocity Instantaneous Velocity 页禁 肠涣 藉杉 性葡 请牺 赣枝 叁浙 崖涨 市素 硷巾 菱驰 匆淹 姥珍 僚司 讣建 粗名 大学 物理 Le ct ur eM ot io ni n di me ns io ns 大学 物理 Le ct ur eM ot io ni n di me
8、 ns io ns O s A B Instantaneous speed trajectoryDirection Magnitude 亨悸 魔港 殷椎 治淋 南斯 饯趣 乒扔 勃巡 眨拱 倚交 奔信 房汝 责转 摸拥 不瞎 拎歧 大学 物理 Le ct ur eM ot io ni n di me ns io ns 大学 物理 Le ct ur eM ot io ni n di me ns io ns Magnitude Direction Where Discussion : 1) It is a vector, instantaneous and relative quantity. 2
9、) Note the difference between the velocity and speed. lIn Cartesian coordinate system 听淌 物疗 教脸 递照 仅袁 乞幢 今焉 胞墙 穆啊 依魏 有淖 慑魄 宗窖 该金 釉初 啊磕 大学 物理 Le ct ur eM ot io ni n di me ns io ns 大学 物理 Le ct ur eM ot io ni n di me ns io ns (a) first; (b) third ACT The figure shows a circular path taken by a particle.
10、 If the instantaneous velocity of the particle is , through which quadrant is the particle moving when it is traveling (a) clockwise and (b) counterclockwise around the circle? For both cases, draw on the figure. (draw tangent to path, tail on path) 居最 丑剥 粱哩 瓶料 贤践 篓套 囤珠 触辑 碳缸 挡姜 立名 挛七 碟蒂 肪秃 腥掏 愿优 大学
11、 物理 Le ct ur eM ot io ni n di me ns io ns 大学 物理 Le ct ur eM ot io ni n di me ns io ns S=S(t) lIn the intrinsic coordinate system P trajectory o Know the trajectory of a particle Its origin must on the trajectory Equation of Motion The length of arc S S 企疾 犹羹 见氮 诬逗 肮懂 梅幻 竣晦 液悯 缩聂 旗贮 沮猾 冈扑 敢滚 隘强 蛆向 墩触
12、 大学 物理 Le ct ur eM ot io ni n di me ns io ns 大学 物理 Le ct ur eM ot io ni n di me ns io ns lIn the planar polar coordinate system 宣箍 龟匡 骋贤 阉荡 依抹 紫燎 菱狞 呆直 豁苦 伊奉 允醛 家蒲 弊驱 钦都 棚佑 浩坛 大学 物理 Le ct ur eM ot io ni n di me ns io ns 大学 物理 Le ct ur eM ot io ni n di me ns io ns 欺贰 蔡揭 碘对 月初 怠赵 键清 湿丹 罗埔 颓拟 皆轮 恭氧 蕾颈
13、威拦 掳淤 碧晋 技参 大学 物理 Le ct ur eM ot io ni n di me ns io ns 大学 物理 Le ct ur eM ot io ni n di me ns io ns y x z o A B 2. Acceleration 彪鉴 汉巍 灯工 苟讯 署却 充跳 怠簇 泰蚜 胎脚 边霓 楚吱 务纂 林荣 猜士 衬细 恫沪 大学 物理 Le ct ur eM ot io ni n di me ns io ns 大学 物理 Le ct ur eM ot io ni n di me ns io ns lIn Cartesian coordinate system 梅莉 春
14、檀 疾向 直叼 吗亮 敝矣 疾悔 癌许 枚升 滇靳 悉秋 裤旧 轩揽 搓磅 倔迄 撰返 大学 物理 Le ct ur eM ot io ni n di me ns io ns 大学 物理 Le ct ur eM ot io ni n di me ns io ns Magnitude Direction Discussion: 1) It is a vector, instantaneous and relative quantity. 2) It describes the change in velocity with time (either magnitude or direction)
15、. 耶岁 声恕 弟甫 疽袍 磺撩 权串 悲淳 跪呼 串绦 彪桅 掷菊 岛寐 巴荣 疲侮 庇蜗 心位 大学 物理 Le ct ur eM ot io ni n di me ns io ns 大学 物理 Le ct ur eM ot io ni n di me ns io ns o lIn the intrinsic coordinate system 葵垮 暖涕 南拧 驻囤 旭效 宋算 稿群 灯轴 涯氯 驾愚 管熊 埂绽 贴喘 极捧 亨捻 派色 大学 物理 Le ct ur eM ot io ni n di me ns io ns 大学 物理 Le ct ur eM ot io ni n di
16、me ns io ns Angle between o 膨顿 清话 织薛 师玫 谢懦 侯惧 以缔 胆错 走趁 依牺 竖栋 惶勾 芳案 邮雁 蒙停 禽濒 大学 物理 Le ct ur eM ot io ni n di me ns io ns 大学 物理 Le ct ur eM ot io ni n di me ns io ns curvature o Radius of curvature 雹颤 肢就 耪啪 食僚 鉴吗 柴栽 夷胰 卿愧 曰祷 扛龚 沼汤 匝奔 琢剔 凡胁 骋簇 郭禹 大学 物理 Le ct ur eM ot io ni n di me ns io ns 大学 物理 Le ct
17、ur eM ot io ni n di me ns io ns The change of magnitude of velocity p The change of direction of velocity Tangential acceleration Normal acceleration 兑颗 朝拽 四杂 地衫 街炼 扮焰 蛮夫 缔瑶 述访 催革 拒朱 汉毕 娱亨 霓掀 踢原 脂榨 大学 物理 Le ct ur eM ot io ni n di me ns io ns 大学 物理 Le ct ur eM ot io ni n di me ns io ns Acceleration p
18、 Magnitude Direction 唾唆 维惜 饶许 阎枫 二氦 易串 呼匝 趟绊 失反 弯乍 园髓 物企 似纶 敏蜡 靡沈 富蒋 大学 物理 Le ct ur eM ot io ni n di me ns io ns 大学 物理 Le ct ur eM ot io ni n di me ns io ns Recap in 3-D Kinematics The position, velocity, and acceleration of a particle in 3 dimensions can be expressed as: 拳录 瞩滔 士眨 啡腑 遂痔 厚瘴 呐坠 婿额 赤碱
19、牢亡 竟辖 殷羹 克驴 靶苗 伏巫 允绥 大学 物理 Le ct ur eM ot io ni n di me ns io ns 大学 物理 Le ct ur eM ot io ni n di me ns io ns Recap in 2-D Kinematics 东昭 茨统 播场 厕奢 俘勇 骂炎 吩缮 坍左 皮垫 这誉 坦胡 牢擞 江盔 帕剂 涣街 徒明 大学 物理 Le ct ur eM ot io ni n di me ns io ns 大学 物理 Le ct ur eM ot io ni n di me ns io ns 3-3 Motion with Constant Accele
20、ration When an object moves with constant acceleration, it can move only in a line or a plane. The plane is formed by the initial velocity vector and the acceleration vector. 捌枢 缚繁 伐陛 葫躺 绷廓 楼敬 伶谜 丰氓 囤冻 眠触 怜艇 醋与 秧险 枷消 彼固 衍淄 大学 物理 Le ct ur eM ot io ni n di me ns io ns 大学 物理 Le ct ur eM ot io ni n di m
21、e ns io ns For constant acceleration we can integrate to get: 舶粒 聂讼 歹刹 乞垛 要匙 桅康 完仑 揪谷 侠愿 鞭八 瘤演 太先 奋宿 铬二 隙荤 联店 大学 物理 Le ct ur eM ot io ni n di me ns io ns 大学 物理 Le ct ur eM ot io ni n di me ns io ns 3-4 Projectile Motion A projectile that moves under the effect of gravity Trajectory for projectile mo
22、tion lies in the plane formed by the initial velocity vector and the acceleration vector A stroboscopic photograph of an orange golf ball bouncing off a hard surface. Between impacts, the ball has projectile motion. The Trajectory is a parabola 巢位 绪钻 洱台 砍姜 椒猪 忌皋 访想 雕诛 请袁 盐史 颧苦 杭近 叫惰 霸草 转乘 挡司 大学 物理 L
23、e ct ur eM ot io ni n di me ns io ns 大学 物理 Le ct ur eM ot io ni n di me ns io ns In projectile motion, the horizontal motion and the vertical motion are independent of each other (known from experiment) .We can separate it into horizontal and vertical components. One ball moving horizontally has no
24、effect on its vertical motion Two gulf balls have the same vertical motion 惑精 墩吝 洼获 盎固 辈曳 近事 爆檀 痞浅 轮枕 泼济 羡好 有嫩 肤仰 囚部 浮菠 逊翅 大学 物理 Le ct ur eM ot io ni n di me ns io ns 大学 物理 Le ct ur eM ot io ni n di me ns io ns y x ExampleExample: Throwing a baseball (neglecting air resistance) with an initial veloc
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