Mechanics II - Dynamics (saylor.org)

Please note: this legacy course does not offer a certificate and may contain broken links and outdated information. Although archived, it is open for learning without registration or enrollment.

Dynamics is a sub-branch of the general field of study known as Mechanics. It is very closely related to—and often combined with—the study of Statics, which you encountered in Mechanics I .

In both Statics and Dynamics, we use Newton’s 2nd Law: F = ma. In Statics, the sum of the applied forces is always zero, thus making the acceleration zero. This was very important to the structures studied in Statics. Catastrophe generally results when structures (like bridges and buildings) accelerate. Very likely you are quite pleased—even if you do not realize it every time—when you cross a bridge that does not accelerate while you are on it, and we have Newton’s First Law to thank for it. Newton’s First Law states that objects will continue to do what they are doing unless unbalanced forces make them do otherwise. This law includes the law equilibrium condition that the moments will also sum to zero, and that there will thus be no rotational acceleration. In Dynamics, the sum of the forces will not necessarily be zero (if it is zero, then the sum of the moments is not). We will thus study accelerated motion.

As with Introduction to Mechanics , we will begin this course by studying the accelerated motion of particles (also known as the Kinematics of Particles). We will only look at what an object is doing (the position, velocity, acceleration)—not why it might be doing that.

In Unit 2, we will take a look at the Kinetics of Particles, or the study of the why of Kinematics. We will want to know how to change the velocity of a particle in order to learn what causes accelerations.

We will then take a step towards the more realistic by considering the size, shape, and orientation of objects as they accelerate. We term this type of motion “Rigid Body Motion.” We begin, in Unit 3, with the Kinematics of Rigid Bodies, looking first at the rotational motion of objects. We will then introduce the possibility that objects can move (and accelerate) translationally and rotationally at the same time. In Unit 4, we will look at sample problems that will help you understand the concepts learned in Unit 1, Unit 2, and Unit 3. Next, in Unit 5, we study the Kinematics of such motion.

In Unit 6, we will look at many of the principles we learned in the first few units-this time, in three-dimensions. We will begin with the three-dimensional Kinematics of a Rigid Body and then finish with three-dimensional Kinetics.

We will complete our study of Dynamics with Unit 7, a look at Vibrational Motion, or what happens when objects oscillate about a neutral state. In Unit 4, we will look at sample problems that will help you understand the concepts learned in Unit 5, Unit 6, and Unit 7.

Upon successful completion of this course, the student will be able to:

- Formulate rectilinear and curvilinear motion in one-dimension.

- Solve projectile motion problems.

- Identify and solve problems with normal, tangential, and cylindrical components for curvilinear motion in one-dimension.

- Formulate relative motion of two particles and relative motion using translating axes for particles in one-dimension.

- Identify Newton’s second law.

- Identify equations of motion for a system of particles in one-dimension.

- Identify equations of motion in rectangular, normal, tangential, and cylindrical components in one-dimension.

- Identify orbital motion and space mechanics.

- Solve work, energy, power, and efficiency for particles and systems of particles in one-dimension.

- Identify energy, potential energy, and conservation of energy for particles and systems of particles in one-dimension.

- Identify impulse, momentum, and conservation of momentum for particles and systems of particles in one-dimension.

- Identify angular momentum, angular impulse, and impact for particles and systems of particles in one-dimension.

- Identify translation and rotation of rigid bodies in two-dimensions.

- Identify absolute and relative motion analysis in two-dimensions.

- Identify Instantaneous Center of Zero Velocity.

- Identify acceleration and rotating axes in two-dimensions.

- Formulate Moment of Inertia for Rigid bodies.

- Identify planar kinetic equations of motion, translation, rotation, and general plane motion for rigid bodies.

- Identify work, energy, and kinetic energy for rigid bodies.

- Compute work done by a force and work done by a couple for rigid bodies.

- Identify work and energy principles and conservation of energy for rigid bodies.

- Identify impulse, momentum, and conservation of momentum for a system of particles.

- Identify impact and eccentric impact for a system of particles.

- Identify kinematics of rigid bodies in three-dimensions.

- Identify general motion and relative motion in three-dimension.

- Identify angular motion and kinetic energy in three-dimension.

- Identify undamped free and force vibrations.

- Identify viscous damped free and forced vibrations.