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Mechanics: Kinematics & Newton's Laws

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Motion, projectiles, circular motion and Newton's laws of motion.

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Kinematics

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  1. 1Kinematics
    A subfield of physics that studies the motion of points, bodies, and systems of bodies without considering the forces that cause them to move
  2. 2Kinematics often called
    The geometry of motion
  3. 3How does kinematics differ from dynamics?
    Kinematics describes motion without forces; dynamics studies the effect of forces on bodies
  4. 4Etymology of the word kinematic
    From A.M. Ampère's cinématique, from Greek κίνημα kinema (movement, motion)
  5. 5Position vector
    A vector drawn from the origin of a reference frame to a particle, expressing both distance and direction
  6. 6Velocity in physics
    The rate of change of position with respect to time, defined as v = dr/dt
  7. 7Instantaneous velocity
    The limit of average velocity as the time interval approaches zero, the time derivative of position
  8. 8Speed
    The magnitude of velocity, always non-negative: |v| = ds/dt
  9. 9Acceleration
    The rate of change of velocity vector, defined as a = dv/dt = d²r/dt²
  10. 10Average acceleration
    The ratio Δv/Δt, the change in velocity divided by the time interval
  11. 11Trajectory
    A vector function of time r(t) that defines the curve traced by a moving particle
  12. 12Displacement
    The difference between two positions of a particle, Δr = r_final − r_initial
  13. 13Is the distance traveled always equal to displacement?
    No, the distance traveled is always greater than or equal to the displacement
  14. 14Relationship between velocity and trajectory
    Velocity is always tangent to the particle's trajectory at every position along its path
  15. 15Relative position vector
    A vector defining the position of one point relative to another: r_A/B = r_A − r_B
  16. 16Relative velocity
    The difference between the velocities of two points: v_A/B = v_A − v_B
  17. 17Constant acceleration equation for velocity
    v = v₀ + at
  18. 18Kinematic equation relating position and time
    r = r₀ + v₀t + ½at² (for constant acceleration)
  19. 19Equation relating velocity and position (without time)
    v² = v₀² + 2a·Δr (for constant acceleration)
  20. 20Cartesian coordinates in kinematics
    A coordinate system using perpendicular x, y, z axes with unit vectors i, j, k
  21. 21Direction cosines
    Components of a unit vector providing a quantitative measure of direction
  22. 22Cylindrical-polar coordinates
    Coordinates using radius r, angle θ, and height z to define position
  23. 23Radial unit vector
    e_r, a unit vector pointing away from the origin in polar coordinates
  24. 24Tangential unit vector
    e_θ, a unit vector perpendicular to the radial direction in polar coordinates
  25. 25Velocity formula in polar coordinates
    v = ṙe_r + rθ̇e_θ (radial and tangential components)
  26. 26Centripetal acceleration
    The component of acceleration pointing toward the center of curvature: −rθ̇²e_r
  27. 27Coriolis acceleration
    The component of acceleration due to the coupling of radial and angular motion: 2ṙθ̇e_θ
  28. 28Angular velocity
    The rate at which the angular position changes with time: ω = dθ/dt
  29. 29Angular acceleration
    The rate at which angular velocity changes with time: α = dω/dt
  30. 30Velocity for circular motion
    v = rωe_θ (tangential velocity)

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