University Physics---Particle Kinematics

There are three coordinate systems in particle kinematics,可以相互转化,Each has different uses,can be used to describe movement.

直角坐标系

Describing motion in the Cartesian coordinate system is basically the same as high school physics.It is mainly to distinguish the following concepts and the connection between them.

• 位置矢量
• 位移
• 平均速度
• 瞬时速度
• 速率
• 平均加速度
• 瞬时加速度
• Orbital equations and equations of motion
• Velocity Equation
• acceleration equation

自然坐标系

组成

The natural coordinate system consists of three parts：

• The trajectory of an object's motion
• 原点
• 正方向

Each point in the natural coordinate system has a corresponding tangential acceleration（Parallel trajectory tangent）和Normal acceleration度（Vertical trajectory tangent）

distance and displacement

• The distance refers to the length of the trajectory from the origin to the current point,是标量

• The position refers to the line from the origin to the current point,是矢量

• The magnitudes of the two are equal only in unidirectional motion with straight trajectories.

Average and instantaneous rates

• Average velocity refers to the ratio of distance to time,是标量

• Average velocity and average speed are not necessarily equal in magnitude,Distance and speed are equal only if they are equal in magnitude.

• When time and distance both tend to0,The average rate of this is the instantaneous rate

• Instantaneous velocity and instantaneous velocity are equal in magnitude

Instantaneous velocity in natural coordinates

• In the natural coordinate system, the velocity of each point is parallel to the tangent direction of the trajectory
• Multiplying the velocity by the tangent unit velocity is the way to express velocity in the natural coordinate system

Acceleration in natural coordinate system

• The acceleration is decomposed into tangential acceleration and normal acceleration and normal acceleration.

• The tangential acceleration is used to control the speed,Normal acceleration is used to change the direction of velocity

• Normal acceleration is centripetal acceleration.

• Orbits are not necessarily circular,But each point has a corresponding arc.

• With tangential acceleration and velocity, the corresponding arc radius can be calculated,称为曲率半径.

极坐标系

Polar coordinate systems are described by angular quantities,The corresponding concept is closely related to the Cartesian coordinate system.

角位移

• Angular displacement is the change in angle
• $位移=半径\ast 角位移$
• Angular displacement is also directional,The direction of the angular displacement follows the right-hand rule

角速度

• Angular velocity is also a vector,Represents the instantaneous rate of change of angular displacement
• $速度=角速度\ast 半径$（Treat as a scalar）
• $角速度=d角位移/d时间$
• If processed as a vector,$线速度=角速度\times 半径$

角加速度

• The instantaneous change in angular velocity during angular acceleration,Linear acceleration cannot be directly obtained from angular quantities,It is necessary to use the concepts in the natural coordinate system.
• $Tangential\; acceleration度=半径\ast 角加速度$
• $Normal\; acceleration度=半径\ast The\; square\; of\; the\; angular\; velocity$
• $加速度=\sqrt{Tangential\; acceleration{度}^2+Normal\; acceleration{度}^2}$

Uniformly variable linear motion formula