Overview
This lecture covers the kinetics of particles in Chapter 13, focusing on Newton’s second law, equations of motion, and example problems using different coordinate systems.
Mechanics of Particle Kinetics
- Kinetics studies the relationship between motion and the forces causing it.
- Focus is on analyzing the motion of particles under applied forces.
Newton’s Second Law of Motion
- Newton’s second law: Force equals mass times acceleration (F = ma).
- Law applies to individual particles and systems of particles.
Equations of Motion (EOM)
- The equation of motion describes how a particle’s velocity and position change due to applied forces.
- EOM can be written as ΣF = ma for a single particle.
- For systems of particles: motion is considered by summing forces and masses for all particles.
EOM in Rectangular Coordinates
- Rectangular coordinates use x, y, and z axes to resolve vector components.
- Acceleration and forces are broken down into respective x, y, and z components for easier calculation.
EOM in Normal and Tangential Coordinates
- Normal and tangential coordinates follow curved paths, with tangential direction along motion and normal direction perpendicular.
- Forces and acceleration can be split into these directions, useful in circular or curved motion analysis.
Example Problems
- Example 1 demonstrates applying EOM in rectangular coordinates for a particle under a known force.
- Example 2 applies EOM in normal and tangential coordinates, involving a 900 lb weight towing two carts.
Key Terms & Definitions
- Kinetics — The study of forces and their effect on motion.
- Equation of Motion (EOM) — Mathematical expression relating forces, mass, and acceleration.
- Rectangular Coordinates — Coordinate system using perpendicular axes (x, y, z).
- Normal and Tangential Coordinates — Directions aligned with and perpendicular to the path of motion.
Action Items / Next Steps
- Complete Homework 3 as assigned.
- Review example problems from Chapter 13.
- Read textbook sections on EOM in rectangular and normal/tangential coordinates.