kinematics

Examples of kinematics in the following topics:

• Defining Kinematics

  • Kinematics is the study of the motion of points, objects, and groups of objects without considering the causes of its motion.
  • The study of kinematics is often referred to as the "geometry of motion."
  • A formal study of physics begins with kinematics.
  • Kinematic analysis is the process of measuring the kinematic quantities used to describe motion.
  • Kinematic equations can be used to calculate the trajectory of particles or objects.

• Constant Angular Acceleration

  • Kinematics is the description of motion.
  • We have already studied kinematic equations governing linear motion under constant acceleration:
  • Similarly, the kinematics of rotational motion describes the relationships among rotation angle, angular velocity, angular acceleration, and time.
  • By using the relationships a=rα, v=rω, and x=rθ, we derive all the other kinematic equations for rotational motion under constant acceleration:
  • Relate angle of rotation, angular velocity, and angular acceleration to their equivalents in linear kinematics

• Applications

  • There are four kinematic equations that describe the motion of objects without consideration of its causes.
  • Kinematics is the branch of classical mechanics that describes the motion of points, bodies (objects), and systems of bodies (groups of objects) without consideration of the causes of motion.
  • There are four kinematic equations when the initial starting position is the origin, and the acceleration is constant:
  • Notice that the four kinematic equations involve five kinematic variables: $d$, $v$, $v_0$, $a$, and $t$.
  • Choose which kinematics equation to use in problems in which the initial starting position is equal to zero

• Problem-Solving Techniques

  • Examine the situation to determine that rotational kinematics (rotational motion) is involved.

• Kinematics of UCM

• Motion with Constant Acceleration

  • Acceleration can be derived easily from basic kinematic principles.
  • Due to the algebraic properties of constant acceleration, there are kinematic equations that relate displacement, initial velocity, final velocity, acceleration, and time.

• Relationship Between Linear and Rotational Quantitues

  • With the relationship of the linear and angular speed/acceleration, we can derive the following four rotational kinematic equations for constant $a$ and $\alpha$:

• The Kinematics of Photon Scattering

• Centripetial Acceleration

  • As mentioned in previous sections on kinematics, any change in velocity is given by an acceleration.

• Parametric Equations

  • A common example occurs in kinematics, where the trajectory of a point is usually represented by a parametric equation with time as the parameter.