University of Colorado at Boulder Home A to Z Map This Site CU Web Site CU People

# Department of Mechanical Engineering

### MCEN 2043 - Dynamics

1. Kinematics of Particles

• Describe the distinction between a particle and a rigid body.
• Define position, velocity, and acceleration of a particle in rectilinear motion. The concepts of position, distance traveled, velocity, and speed should be understood, and not confused.
• Write the relationships between position, velocity, and acceleration of a particle in rectilinear motion, under general conditions, as a function of time. Solve for two of them, given the third, by differentiation and/or integration. This requires an understanding of the appropriate initial conditions in each case.
• Describe the physical interpretation of position, velocity, and acceleration of a particle.
• Identify and analyze special cases of rectilinear motion (uniform motion, uniformly accelerated motion).
• Write the relationships between position, velocity, and acceleration of a particle in curvilinear motion, under general conditions, as a function of time using vector notation.
• Compute the derivative of a vector function and compute the components of vector fields in Cartesian, path, polar, and cylindrical coordinate systems. Use these concepts to analyze problems of projectile motion in both two-and three-dimensions.
• Describe the concept of relative motion and compute position, velocity, and acceleration of particles in relative motion and dependent relative motion.

2. Kinetics of Particles: Newton's 2nd Law

• Define mass and linear momentum and explain the concept of a Newtonian reference frame.
• Write and explain Newton's 2nd Law of motion.
• Write and explain Newton's 2nd Law of motion, and explain the concept of conservation of momentum.
• Systematically use Newton's second law to analyze the motion of a particle acted upon by forces that are constant, and explicit functions of time, position, and velocity. Identify the appropriate initial conditions in each case, and describe physical examples of each case. This should be done for both rectilinear and curvilinear motion.
• Describe the concept of angular momentum of a particle, write Newton's 2nd law in terms of angular momentum, and describe the principle of angular momentum.

3. Kinetics of Particles: Energy and Momentum Methods

• Define and compute the work of a force and the kinetic energy of a particle. Develop the principle of work and energy.
• Apply the method of work and energy to problems involving a single body or connected bodies.
• Define conservative forces, potential energy, and the principle of conservation of energy. Identify mechanical loss mechanisms. Apply the principle of conservation of energy to problems involving a single body or connected bodies.
• Define the concept of linear impulse and derive the principle of impulse and momentum.
• Apply the principle of impulse and momentum to problems of direct and oblique central impact.
• Select the method of analysis that is best suited for the solution of a given problem (Newton's Law, Work and Energy, Impulse and Momentum) and the combination of these methods.
• Develop the fundamental dynamics equations and principles for a system of particles.

4. Two-Dimensional Rigid-Body Kinematics

• Define the fundamental types of plane motion.
• Derive relations defining the velocity and acceleration of any particle on a rigid body for translation and rotation about an axis in two- and three-dimensions.
• Decompose general plane motion into the sum of a translation and a rotation.
• Define and compute the instantaneous center of rotation.
• Describe and analyze the plane motion of a particle relative to a rotating frame. Determine the Coriolis acceleration in plane motion.

5. Two-Dimensional Rigid-Body Kinetics

• Solve problems in two-dimensional rigid-body dynamics, regardless of their kinematic characteristics, by equating the sum of the forces acting on the rigid body to the vectors ma and omega. To effect this solution, construct appropriate free-body diagrams.
• Define the work of a couple and the kinetic energy of a rigid body.
• Apply the method of work and energy to the plane motion of a rigid body.

Catalog Description

Dynamic behavior of particle systems and rigid bodies; 2-D and 3-D kinematics and kinetics; impulse, momentum, potential and kinetic energy, work and collision. Lectures and homework assignments involve computer work and hands-on laboratory work in the ITLL, documented by written reports.

Prerequisites: MCEN 2023

Prepared by M. Dunn and J. Zable