Fundamental Principles of Kinematics and Vector Motion

Introduction to Kinematics

Kinematics: A branch of physics which studies physical movement, irrespective of the causes that produce it. To study motion, a reference system is required.

Velocity and Acceleration

• Average Velocity (Speed M): A vector considered as the ratio between the displacement vector and the interval of time. It is measured in m/s and has the direction of the displacement.
• Instantaneous Velocity: The limit of the average speed when the time interval approaches zero (tangent to each point of the trajectory).
• Average Acceleration: A vector representing the ratio between the increase in speed and time.
• Instantaneous Acceleration: The limit of the average acceleration as the time interval approaches zero; it is the derivative of the velocity vector with respect to time.

Intrinsic Components of Acceleration

Intrinsic Components: Tangential and normal acceleration are the projections of the acceleration on the tangent and normal at each point of the trajectory.

• Tangential Acceleration (At): The module represents the change in speed.
• Normal Acceleration (A.normal): Represents the change in the direction of velocity.

Scalars and Vectors

• Scalars: Magnitudes that are perfectly defined by their numerical value.
• Vectors: Magnitudes that must be defined by their numerical value, direction, and sense; they are represented by vectors.

Vector Characteristics and Position

Vector: A line segment between two given points in a certain order. Characteristics of a vector include magnitude, direction, sense, and point of application.

• Unit Vector: A vector with a module of one. Therefore, it only indicates direction and sense. As a result, every vector "u" can be written as a product of its magnitude by a unit vector "u" in its direction. The unit vectors in the directions of the coordinate axes are i, j, and k.
• Position Vector (V position): A vector that has its origin at the center of the reference system and its end at the position of the mobile object at the moment considered.
• Displacement Vector (V shift): Given two positions, the displacement vector has its origin at the starting position and its end at the final position.

Motion, Trajectory, and Frequency

Path: The road followed by the mobile object. Average Speed: The ratio of the space covered to the time elapsed between two positions. Instantaneous Speed: The average speed limit when the time interval approaches zero.

• Scalar Product: A scalar that equals the product of the modules by the cosine of the angle.
• Period: The time it takes for the mobile object to complete a full turn.
• Frequency: The number of turns completed in one second.