kinematics chapter

Kinematics

• Definition: Study of the motion of objects without considering the forces that cause the motion.
• Key concepts:
  • Displacement (Δx): The shortest distance between the initial and final positions of an object.
  • Distance (d): The total length of the path traveled by an object.
  • Speed (v): The rate of change of distance with time.
  • Velocity (v): The rate of change of displacement with time.
  • Acceleration (a): The rate of change of velocity with time.

Newton's Laws of Motion

• First Law (Law of Inertia):
  • An object at rest will remain at rest, and an object in motion will continue to move with a constant velocity, unless acted upon by an external force.
• Second Law (F = ma):
  • The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.
• Third Law (Action and Reaction):
  • For every action, there is an equal and opposite reaction.

Momentum

• Definition: The product of an object's mass and velocity.
• Conservation of momentum: The total momentum of a closed system remains constant over time.
• Collisions:
  • Elastic collision: Momentum is conserved, and kinetic energy is also conserved.
  • Inelastic collision: Momentum is conserved, but kinetic energy is not conserved.

Energy

• Kinetic Energy (K): The energy of motion, given by K = (1/2)mv^2.
• Potential Energy (U): The energy of position or configuration, given by U = mgh for gravitational potential energy.
• Conservation of Energy: The total energy of a closed system remains constant over time.

Rotational Motion

• ** Angular Displacement (Δθ)**: The angle through which an object rotates.
• Angular Velocity (ω): The rate of change of angular displacement with time.
• Angular Acceleration (α): The rate of change of angular velocity with time.
• Torque (τ): A measure of the rotational force that causes an object to rotate.
• Rotational Kinetic Energy: The energy of rotational motion, given by K_rot = (1/2)Iω^2.

运动学

• 运动学定义：不考虑引起运动的力，研究物体的运动。
• 关键概念：
  • 位移（Δx）：物体从初始到最后位置之间的最短距离。
  • 距离（d）：物体运动的总路径长度。
  • 速度（v）：距离随时间变化的速率。
  • 角速度（v）：位移随时间变化的速率。
  • 加速度（a）：速度随时间变化的速率。

牛顿运动定律

• 第一定律（惯性定律）：
  • 静止的物体将保持静止，而运动的物体将继续以恒速度运动，除非受到外力作用。
• 第二定律（F = ma）：
  • 物体的加速度与作用于其上的净力成正比，和其质量成反比。
• 第三定律（作用和反作用）：
  • 对于每一个作用，总有一个相等而相反的反作用。

动量

• 定义：物体的质量和速度的乘积。
• 动量守恒：闭系中的总动量保持不变。
• 碰撞：
  • 弹性碰撞：动量守恒，动能也守恒。
  • 非弹性碰撞：动量守恒，但动能不守恒。

能量

• 动能（K）：运动的能量，计算公式为 K = (1/2)mv^2。
• 势能（U）：位置或配置的能量，计算公式为 U = mgh（引力势能）。
• 能量守恒：闭系中的总能量保持不变。

旋转运动

• 角位移（Δθ）：物体旋转的角度。
• 角速度（ω）：角位移随时间变化的速率。
• 角加速度（α）：角速度随时间变化的速率。
• 力矩（τ）：引起物体旋转的旋转力。
• 旋转动能：旋转运动的能量，计算公式为 K_rot = (1/2)Iω^2。