Mechanical PE Exam Topic Concepts

The Key to Understanding Engineering Dynamics

What are the best steps for understanding engineering dynamics?

Dynamics is often difficult for engineering students (or even engineers).  But there is a very important key to understanding engineering dynamics.  The key is to focus on a systematic approach to solving dynamics problems. This blog post will explain how to use the systematic approach.

Understanding Engineering Dynamics Categories

You may have noticed that there can be many different ways to solve any given dynamics problem.  I have taught dynamics several times in my academic career, and I have noticed that students have a hard time finding the best method to use for a given problem.

Any dynamics problem will fall into one of four categories:

  1. Particle kinematics
  2. Particle kinetics
  3. Rigid body kinematics
  4. Rigid body kinetics

The key for fully understanding engineering dynamics and solving dynamics problems is to identify the proper category and understand the solution procedure for that category.

understanding engineering dynamics

Particles and Rigid Bodies

The first step to understanding engineering dynamics problems is to know the difference between particles and rigid bodies. It is common to hear the word particle and automatically assume something small.  However, that is not necessarily the case. In dynamics problems it is not uncommon to have something like a car or train be a particle. The defining difference between particles and rigid bodies is rotation. If the object is not rotating about its own centroid it can be treated as a particle because the object’s rotational properties do not matter. If the object is rotating about its own centroid, the rotational properties are important and it is considered a rigid body.

Kinematics and Kinetics

One very important area in understanding dynamics is the distinction between kinematics and kinetics. The determining factor here is force. Kinematics problems concentrate on motion without any regard to the force required for that motion. In other words, kinematics focusses on the geometry of motion.  Kinetics problems involve forces.

The Systematic Approach to Understanding Engineering Dynamics

So, now we can put some ideas together and define the systematic approach. When you read a dynamics problem, the very first step is to ask yourself ‘is this problem dealing with particles or rigid bodies?’. Remember, if the object is not rotating about its own center of mass it is a particle. Also, rigid body problems will give additional information about the object such as moment of inertia.
Once you determine if the problem relates to particles or rigid bodies, the next step is to ask ‘is this a kinematics or kinetics problem?’. Force is the key here.

Let’s look at some examples:

Example 1

The 5 inch diameter disk shown rolls on a surface without slipping. The velocity of point O is 1.5 ft/s to the right. For the position shown calculate the absolute velocity of point P.
understanding engineering dynamics

So, the first thing we need to determine is if this is a particle or rigid body problem. Because the disk is rotating about its own center of mass it is a rigid body. The next step is to determine if the problem is in the category of kinematics or kinetics. The problem only asks about the motion (position and velocity for this problem) and does not ask or include information about forces. Therefore, the problem is a kinematics problem. Now we know the problem is a rigid body kinematics problem.

Example 2

A man completes a long jump of a distance of 21 feet. He has a horizontal velocity of 28 ft/sec at the time of takeoff. What is the vertical velocity at takeoff?
This problem does not include any rotation about the center of mass for the man. Also, notice the problem did not provide any information about the man (mass, center of gravity location, etc.). Therefore, the man can be considered a particle. The problem only includes information about motion (position and velocity) with no information about forces. So, the problem is a kinematics problem. Now we know the problem category is particle kinematics.

Example 3

A 70 kg box slides down a ramp that has an angle of 20 degrees from the horizontal and has a coefficient of kinetic friction of 0.30. The box is given an initial velocity of 3 m/s. Calculate the velocity of the box after it travels 8 meters down the ramp.
The box in this problem is not rotating about its center of gravity, so it can be treated as a particle. The question only asks for velocity, but there is a force involved in the question. The force of friction will be slowing down the box. Because a force is involved in the solution, the question is a kinetics problem. So, the problem is in the category of particle kinetics.

Example 4

The connecting rod AB for the piston assembly shown weighs 1.4 lb. The center of gravity is located 7 inches from point B, and the radius of gyration about the center of gravity is 2.5 inches. The piston head weighs 2.4 lbs. The engine is running at a constant speed of 2400 rpm. Calculate the force on the piston pin at B for the position shown.
 understanding engineering dynamics

The problem involves a piston connecting rod that is rotating about its own center of mass (it is in general plane motion). The problem also gives information about the center of mass location and the radius of gyration (which will give moment of inertia). Therefore, the problem is a rigid body problem. The question specifically asks for force, which is a kinetics problem. So, the problem is a rigid body kinetics problem.

What’s Next?

Understanding engineering dynamics first requires the ability to determine the type of problem to be solved. This blog was all about understanding the four categories. You should be able to read a dynamics problem and identify the proper category. Future blogs will go through solution methods for each category.

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