The topic of kinematics in general, is an interesting topic for learning about and understanding since it includes a variety of subtopics that can be integrated through physics. This research topic can help people predict the motion of an object depending on the surface it rolls on, its density, its shape, its mass, and its volume. It interested me to find out/explore the wide perspective in predictions that come up when researching about kinematics of any rolling object, and how many factors are dependent and affect one another simultaneously. It’s important to comprehend how many laws and forces acting upon an object can lead for individuals to potentially predict the behavior of any rolling object of any size or shape, by considering the center of mass, speed, acceleration, distance traveled, and time-frame.

My prediction or thought for hypothesis is that, as the group of factors such as motions in the geometry of motion as kinematics act upon the rolling object many other consequences come into place that affect the behavior of that object, from the factors that would affect the object, we would be able to predict how the object would react to the kinematics of it rolling on a plane. Forces can be exerted by one to another through contact or any distance. The effect of different forces will help us predict the behavior it will have on those objects. With a larger number of kinematics and forces acting upon the rolling object, it can be easier to analyze the behavior of one and conclude why they affect each other in that way simultaneously. As learnt, there are various kinematics factors, which are, the initial velocity(Vi), (always 0), the final velocity(Vf); the speed of an object after a certain period of time.

Acceleration (a), which is defined as the rate at which the rolling object changes its velocity. The rolling object accelerates if its velocity is changing, increasingly or decreasingly. Time, which is represented as (t), and change of position, which is represented as (x). This research topic links to the global context of Scientific and technical innovation matches well, since this revolves around the comprehending and understanding of kinematics that can affect our ability to predict and think of how a rolling object would react and what factors would it be affected by in which ways, this also relates to science, through physics, and kinematic equations, with algebra. This topics links to a lot of subtopics that I learnt about in the past and had knowledge of, such as forces, friction, gravity, velocity, acceleration, speed, distance, and how each is measured. These sub topics were learnt in physics and the basic terminology has helped through the understanding of explanations and predictions of objects’ behavior in different scenarios while rolling on a flat plane. In mathematics, lessons learnt, such as algebra, and geometry, which helped simplify the logic sense and knowledge of kinematics translating into the rolling of objects.

Through long research, and extensive effort for knowledge, the kinematics of rolling provides for the investigator to easily analyze the behavior of the object as it rolls. Dynamics of a body such as a ball, apple, or a rock is dependent on a number of factors. When an object of a figure or particular dimension is rolling, it is made up of a combination of rotational and translational motion. Kinematics is looked as the motion without all the other forces affecting it. If an object is placed to roll on a flat plane without slipping, the direct contact between them doesn’t move. When using kinematics to help understand the behavior of a rolling object while it is rolling on the plane, angular velocity is introduced, where it is a number that describes its kinematics in its circular motion shown, the immensity is equal to its angular speed of that object, and its direction is perpendicular to the flat plane of its round motion.

Another term is also signified, which is the linear velocity, this is the vector number that indicates the rate of change if position relating to the time of the particle figure’s center of mass. When for example a wheel is rotating on a flat horizontal surface, it is of course rolling at a specific speed (v), it would also rotate about its axis, within an angular speed. Speaking in a logical state, when driving a car, the faster it goes, the faster the wheels turn, therefore, the relationship between linear velocity and angular velocity, can be analyzed where this wheel is moving at a distance (x), as well as at the same time, rolling at an angle. The length of the arc in the wheel or other such circular object is equal to the angle of the segment multiplied by the object’s radius (R). Also, the length of the arc, is equal to the distance the object has traveled over a period of time, since the wheel always has constant direct contact with the plane.

As said before, there is a relationship between angular and linear velocity. When a circular object rotates, within its instantaneous axis, which is the fixed point to the object while it moves, that always begins at zero velocity at a specific period of time. Therefore, when the object moves forward or backward, the axis would move with it at the same time. The motion or kinematics of this body or object is factorized of the motion of translation of the center of gravity, and with it as, the full and entire mass of that rolling object, and as well as, the rotation of the object about the axis through the center of gravity. The linear velocity and acceleration are calculated by considering the forces acting upon it through the center of gravity. As well as calculating the angular velocity and acceleration, which is by using the torques, (it’s the force that causes rotation to occur within objects such as wheels). Also, the moment of inertia, (which is the amount of force of rotation “torque”, that is needed to cause the rate of change in the angular velocity, it can also be defined as the mass of the object to any type of rotational system).

Kinematics includes many different types of motions, the most significant types are the translational motion, oscillatory motion, and rotational motion. Translational is where the object has had a change in location, that means that the object has travelled a specific distance from one point to another. Oscillatory involves the type of motion in which the rolling object is moving through two points, and takes a fixed amount of time for it to occur, it is seen as a periodic and repetitive. The rotational motion, is where a rolling object, rolls. It is a motion that allows this object to move in a direction with a rolling movement around its points.

In kinematics, a set of equations are used, there are four different ones (x - represents displacement which can also be symbolized as d):

x=1/2(Vi+Vf) t

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Vf=Vi+a

x=Vi t+1/2at^2

Vf^2=Vi^2+2ax

These equations can be used to figure and solve a missing variable, in most unknown problems when an object in rolling, three variables would be given and the other variable would be asked to be solved, logic factors are used to address which equations Is the most suitable to be used when solving the problem.

The behavior of objects, when usually conducting an investigation, to analyze, test and conclude a series of data or information, in mathematics, it’s important to always understand and write down notes before analyzing and formatting all information and ideas into an essay. Also, many logical rules and bindings helped the acknowledgment of this topic and research question, many sub-topics built up when reading about this topic, and many wonders and confused thoughts came to life, but through managing time and thoughts, the ability to write and format and essay was motivational when a series of different lessons taken in mathematics were thought of, equations, algebra, geometry, relationships, etc.

With the use of kinematics, to find out the velocity, angle, acceleration, radius, time period, and distance the object traveled, it is easier to predict the behavior of the rolling object, for example, since kinematics depends on motion of objects, its motion can be interpreted to predict the object’s behavior and its factors affecting it. In kinematics, if velocity increases, then the period of time would decrease, as well as, its behavior when friction occurs, and affects the motion of velocity it rolls at. Dynamics is the study of motion with the causes that come a long with it like forces or torques, while kinematics is the study of motion without considering the factors of causes.

Therefore, kinematics does not interpret or relate to any forces that affect the rolling ball when moving, the motion of an object, however can be predicted by using newton’s second law of motion that’s acted on by other forces. The law consists that the acceleration of the object is directly proportional to its net force which is applied and inversely proportional to the mass. Rotational and translational motion is contained by the force of gravity acting upon the round object for it to roll on the plane.

Determining the behavior of a rolling object is not only determined by visual signals, also to prior information about object kinematics within the investigation. The behavior of an object can be determined by observing and analyzing how it reacts to certain factors such as distance, friction, radius, etc., also determined by kinematics, predicting its message passing. So, rotational kinematics also has factors when a rolling object is moving such a tire, when velocity, acceleration Is related, other forces like friction will affect it, such as the speed, velocity, distance it travels, etc.

Overall, my hypothesis was partially correct as through that I have predicted, that some factors can affect the behavior of the objects when kinematics of the objects is shown, such as velocity, acceleration, radius of the object, etc. Although the topic of kinematics isn’t related to any other forces acting upon the object, by analyzing the kinematic variables of it, there is a chance where we can predict other factors that help the ball move increasingly or decreasingly, in which direction, friction, gravity, etc.

There were couple limitations that had to be faced during the research and collecting the findings, one of the main factors, was that, this topic was new to write about, kinematics is not an easy topic, there were many equations and many new key terminology that had to be researched and understood bit by bit, it wasn’t easy to learn about a whole new lesson individually, but, by managing time, breaking down different perspectives subtopics of this essay, there was an ability and motivation to write about something new, and explain a physics topic. By using organization skills and watching videos about the topic, it was easier to understand, and faster to follow through about all the other subs.