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# Understanding Kinematics From Harvey’s Text

In Physics, kinematics (aka coordinate science) is the study of how the motion of an object affects the position and acceleration of that object at any point in space. A kinematic system may be one that is rigid or one that is flexible. Rigid systems have no ‘free motion’ in their interior, while flexible ones exhibit ‘free motion’ at some interior but not at all in their exterior. A system of rigid kinematics has a unique concept: the system’s momentum will ‘cascade’ from the most exterior points to the inside. Thus, for instance, if you take a system of rigid kinematics and take it to the first point where it meets the Earth (where the momentum becomes zero), you will find yourself accelerating downhill; and, if you take the same system and place it on the Earth’s surface, you will find yourself ascending back up.

This is called the Kinematics Law of Universal Acceleration. It can be used in various situations to describe motion and the effects that motion has on objects at various rest states. Of course, it describes both acceleration and the orientation in which an object moves. However, it does so in such a way as to make clear the key points of focus for specific purposes.

One of the first key terms that are crucial to understand for anyone learning about kinematics is time-step. Time-step refers to the difference between instantaneous and steady-state velocity. It can be thought of as a sort of parameter, which can be altered or measured, according to needs. In other words, time-step measures the difference between the speed of an object that has passed through a reference frame, and the velocity that it would have experienced if it had continued to move in the original reference frame. Time-step can also be thought of as the velocity that an object would have experienced if it was in freefall, or simply in a resting condition. Many advanced students are familiar with the concept of time-step, but not with its application to kinematics.

Another of the key takeaways from this section is that there are three main types of displacement. These are referred to as principal, derivative, and integral. Principal displacement occurs when an object has momentum and is moving with respect to the velocity it is exerting. The derivative and integral terms are the ones associated with gravity, impulse, and displacement. It should be easy to see that these terms are all related to one another and all have their own individual meaning.

An important topic that makes up a large part of the Math class of Harvey I’ve Ph.D. is the Study of Kinematics. In this chapter, he covers topics such as:

The topics mentioned in the previous section are important to the student who is preparing to learn about the force of gravity on an object. This is important because it shows the relationship between the time-step derivatives of velocity and the time-step derivatives of the kinetic energy, or in other words, how to express the force of gravity on an object. The next topic that will help a student understand the relationship between time-step derivatives of scalars and momentum is discussed in lecture 6. This topic is called the differential formula for momentum, which can be used to determine the magnitude of an object based on the difference in its velocity and its acceleration at different times.

Students will need to be familiar with the concepts of kinematics, momentum, and the differential formula so that they can properly apply it to real life situations. It is important to remember that, since the velocity and acceleration are directly related, you must be able to convert between the two, and Harvey’s text provides a great deal of information regarding doing just that. There are many other important concepts that are taught in Physics class such as angular momentum and the law of conservation of energy, but students should understand kinematics and momentum well enough to be able to learn about them by themselves.

Kinematics is not a science in the strictest definition, but it is a process that are necessary for any motion that has a source of acceleration to occur. In simpler terms, kinematics can be described as the laws of Physics that describe the way that an object moves with respect to its reference frame. The key takeaways from this text include introducing different terms that students may not have learned before, explaining the relationship between velocity and acceleration, and introducing a process of converting between time and velocity. Overall, this text is a great introduction to an important subject that students should feel comfortable with. While it does have several tedious topics, learning how kinematics relates to other concepts such as mechanics and kinetics will make the student more well-rounded when learning to study Physics.

Understanding Kinematics From Harvey’s Text
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