Embedded Files
⚙️ Module 2: Particle Kinetics
⚙️ Module 2: Particle Kinetics
Understanding Motion Through Forces, Energy, and Momentum
Understanding Motion Through Forces, Energy, and Momentum
Particle kinetics is the study of the relationship between the motion of a particle and the forces acting on it. While kinematics describes how a particle moves, kinetics explains why it moves in that manner by relating forces, mass, velocity, acceleration, work, and momentum.
The animations in this module use carefully selected problems to demonstrate the fundamental principles of particle kinetics and show how they are applied to physical systems. Each animation connects the governing equations with the corresponding free-body diagram, motion, and physical interpretation.
Use the navigation menu to explore the available problem-based animations. Additional topics will be added as the animation library continues to grow.
A General Approach to Particle Kinetics Problems
A General Approach to Particle Kinetics Problems
Most particle kinetics problems can be approached systematically. The specific equations may differ depending on the problem, but the overall workflow remains the same.
1. Choose an Appropriate Coordinate System
1. Choose an Appropriate Coordinate System
Identify the coordinate system that best represents the particle's motion and the geometry of the problem.
Examples include:
Rectangular coordinates
Normal–tangential coordinates
Plane polar coordinates
The choice of coordinates should simplify the description of the motion and the resolution of forces.
2. Draw the Free-Body Diagram
2. Draw the Free-Body Diagram
Isolate the particle and identify all external forces acting on it.
The free-body diagram provides the basis for applying the equations of motion. Each force should be represented with its correct magnitude and direction.
3. Establish the Kinematic Relations
3. Establish the Kinematic Relations
Before applying the kinetics equations, determine the particle's absolute (inertial) acceleration from the appropriate kinematic relations.
Depending on the coordinate system, this may involve relations such as:
aₓ = d²x/dt²
aₜ = dv/dt
aₙ = v²/ρ
aᵣ = r̈ − rθ̇²
aθ = rθ̈ + 2ṙθ̇
The acceleration used in Newton's Second Law must be the actual absolute acceleration of the particle, expressed in the chosen coordinate directions.
⚠️ DO NOT USE PSEUDO-FORCES: Relative motion may make the acceleration expression more complicated, but it does not introduce additional forces. First determine the absolute (inertial) acceleration from the appropriate kinematic relations, and then apply the kinetics equations using the actual forces acting on the particle.
4. Apply the Appropriate Kinetics Principle
4. Apply the Appropriate Kinetics Principle
Once the forces and kinematic relations have been established, select the most suitable kinetics principle.
Newton's Second Law
ΣF = m a
Work–Energy Principle
ΣW1-2 = E2 − E1
Impulse–Momentum Relation
∫F dt = m v2 − m v1
The appropriate method depends on what is known, what is required, and how the forces and motion vary during the problem.
🎥 Available Animations
🎥 Available Animations
Relating the resultant force acting on a particle to its acceleration through a representative dynamics problem.
Relating the work done by forces to the change in kinetic energy of a particle.
Understanding how forces acting over a time interval produce a change in linear momentum.
Analysing short-duration collisions using conservation of momentum and the coefficient of restitution.
📖 Example Problem Sets
📖 Example Problem Sets
(Courtesy of Prof. Suman Dutta)
Page updated
Google Sites
Report abuse