Understanding Motion: A Comprehensive Guide to Kinematics

Posted on Nov 7, 2024 in Physics

1. Uniform Motion

A. Uniform Straight Motion (USM)

Description:

Motion along a straight path with constant speed and velocity. No change in direction. Acceleration is zero (a = 0 m/s²).

Formula:

v = Δs / Δt
s = s₀ + vt

Graphs:

  • Position-time (s-t): Position on the y-axis and time on the x-axis.
  • Speed-time (v-t): Speed on the y-axis and time on the x-axis.

B. Uniform Circular Motion (UCM)

Description:

Motion along a circular path. Constant change in direction. Acceleration is normal or centripetal. Angular motion magnitudes are used.

Angular Magnitudes:

  • θ: Angular displacement (angle): Angle rotated by the radius. Measured in radians (rad). θ = 1 rad when arc and radius are equal.
  • ω: Angular velocity: Angular displacement per unit of time. Units: rad/s (SI) and revolutions/min.

Relationship between Angular and Linear Magnitudes:

  • Linear displacement (s) and angular displacement (θ): s = θr
  • Linear speed (v) and angular speed (ω): v = ωr

Formula:

θ = θ₀ + ωt
ωt = θ – θ₀
θ = ωt (when θ₀ = 0 rad)

  • θ: Final angular displacement (rad)
  • θ₀: Initial angular displacement (rad)
  • ω: Angular velocity (rad/s)
  • t: Time (s)

2. Uniformly Accelerated Straight Motion (UASM)

Features:

Motion along a straight path. Speed is not constant, either increasing or decreasing. Uniform change in speed. Constant acceleration (a ≠ 0).

Formula:

a = (v – v₀) / t
v = v₀ + at
s = s₀ + v₀t + ½at²

  • s: Final position (m)
  • s₀: Initial position (m)
  • v₀: Initial speed (m/s)
  • t: Time (s)
  • a: Acceleration (m/s²)

Reference System and Kinematics

A coordinate system is used to describe motion. Kinematics is a branch of physics that analyzes motion without considering its causes. It originated with Galileo.

Vector Magnitude

To fully define a vector magnitude, we need to know its unit, point of application, magnitude, direction, and sense. Vector quantities include displacement, velocity, acceleration, and force.

Position, Displacement, Distance, Speed, and Acceleration

  • Position (s): Vector magnitude indicating the exact location of an object with respect to the origin of the reference system.
  • Displacement (Δd): Difference between the final and initial positions. Vector magnitude measured in meters.
  • Distance (d): Length of the path traveled by an object. Measured in meters.
  • Velocity (v): Displacement per unit of time. Vector magnitude measured in m/s.
  • Speed (v): Distance per unit of time. Measured in m/s.
  • Average Speed: Total distance divided by total time.
  • Instantaneous Speed: Speed at a specific moment in time.
  • Acceleration (a): Change in velocity per unit of time. Vector magnitude measured in m/s².