Kinematics

Geometric and temporal description of particle and body motion along various trajectories.

General idea of the topic

Kinematics describes motion without asking about its causes. Position, velocity and acceleration as functions of time are enough to describe any trajectory, and one can move from one to another by differentiating or integrating.

The block defines the kinematic quantities and their graphical analysis, studies the simplest motions (rectilinear, circular and rotational), explains how the description changes with the observer and combines the coordinates in two-dimensional motion.

What you will truly understand

By the end you will be able to describe and analyze rectilinear, circular and parabolic motions, interpret position against time and velocity against time graphs and change reference frame.

You will also be able to choose the motion model that best represents a situation.

Recommended learning route

  1. Kinematic Quantities: position, displacement, velocity and acceleration, and their units.
  2. Graphical Analysis of Motion: slopes and areas in position against time, velocity against time and acceleration against time graphs.
  3. Rectilinear Motion: uniform motion, uniformly accelerated motion and vertical fall.
  4. Circular Motion: uniform and non-uniform circular motion.
  5. Rotational Motion: rotation of a body about an axis and its relation to linear motion.
  6. Relative Motion: velocities between observers, pursuit and interception.
  7. Motion in Two Dimensions: horizontal and oblique projectile motion with composition of motions.

Physical criterion you must acquire

The essential criterion is to decide first what type of motion there is: uniform, with constant acceleration, circular or compound. The applicable equations follow from that choice. In two dimensions, each coordinate is an independent motion, linked by time.

Connection with real problems

  • traffic, trajectories and road safety.
  • ball sports and throws.
  • navigation and vehicle control.
  • foundation of dynamics.

Final goal of the topic

The final goal is to describe any motion quantitatively, choose the appropriate model and interpret position, velocity and acceleration both in formulas and in graphs.

Topics in this section

  • Kinematic Quantities

    Fundamental physical quantities to describe position, change of position, and the temporal evolution of motion.

  • Graphical Analysis of Motion

    Technical interpretation of motion using position–time, velocity–time, and acceleration–time diagrams in kinematic contexts.

  • Rectilinear Motion

    Position, velocity, and acceleration in uniform and uniformly accelerated rectilinear motion.

  • Circular Motion

    Angular velocity, centripetal and tangential acceleration in circular paths.

  • Rotational Motion

    Rotational kinematics: angular displacement, velocity, and acceleration in rigid bodies.

  • Relative Motion

    Galilean transformations of position and velocity between reference frames in relative motion.

  • Motion in Two Dimensions

    Projectile motion and planar trajectories combining independent orthogonal components.