Understanding Motion: Reference Systems, Velocity, and Acceleration
Reference Systems and Motion
Reference System: To determine the position of a point at any time, it’s necessary to fix a point in space as a reference. The chosen reference point is taken as the origin (0) of three Cartesian axes, forming a Cartesian framework. Thus, the position of point P will be determined by the coordinates x, y, and z of that point.
Path: The path is the locus of successive positions taken by a moving point in space.
Position: The position of a point P is its location in space and can be reached by 3 Cartesian coordinates or by a vector r (also denoted as OP), which connects the origin of the reference system with point P. This vector is called the position vector. A vector is unitary when its magnitude is 1.
Displacement: Displacement has its origin at the starting point or initial position and ends at the point of arrival or final position (vector) P0P1. It’s calculated as the final position minus the initial position.
Distance Traveled: Distance traveled is the length of the path followed by the moving object. It’s a scalar quantity that matches the magnitude of the displacement only when the motion is rectilinear and doesn’t change direction.
Velocity and Acceleration
Average Velocity: Average velocity is defined as the displacement experienced by the moving point per unit of time. It’s a vector that results from dividing the displacement by the time interval and has the same direction as the displacement vector, since time is a positive scalar.
Instantaneous Velocity: Instantaneous velocity is the velocity of a particle at any given time or at a particular point of the trajectory. Instantaneous velocity is a vector whose magnitude is called speed and represents the space described in the unit of time, whose direction is tangent to the path and coincides with the direction of motion.
Acceleration: In general, acceleration is the variation of velocity over time.
Average Acceleration: The average acceleration vector is defined as the result of dividing the variation of velocity that has occurred in a time interval by the value of this interval.
Instantaneous Acceleration: Instantaneous acceleration is the limiting value that the average acceleration takes when the interval of time is extremely small. This is called the derivative of the velocity vector over time.
Tangential Acceleration: Tangential acceleration is due to the variation of the speed or the speed’s magnitude.
Normal Acceleration: Normal acceleration is due to the changing speed and direction and is called centripetal acceleration.
Types of Motion
Rectilinear Motion: Rectilinear motion is characterized by a straight-line trajectory. Therefore, the direction of the velocity is constant. A mobile has MRU (Uniform Rectilinear Motion) when moving in a straight line without acceleration, and the velocity is kept constant. In this movement, average speed coincides with instantaneous speed.
MRUA (Uniformly Accelerated Rectilinear Motion): MRUA is characterized by constant acceleration. Therefore, both average and instantaneous acceleration match.
Free Fall: Free fall is the movement of a body under the action of gravity, neglecting air resistance. Free fall is uniformly accelerated rectilinear motion.
Circular Motion: Circular motion is characterized by its trajectory being a circle. If we take the center of the circle as a reference point, the position vector of the particle rotates, changing direction every minute, although its magnitude remains constant. The angular velocity (omega) is defined as the angle rotated by the position vector in the unit of time.
MCU (Uniform Circular Motion): This movement is characterized by the circumference being traversed with the same speed, i.e., the magnitude of linear speed remains constant at all times and remains tangent to the trajectory.
Frequency: Frequency is the number of revolutions made in one second (the period and frequency are reciprocals).
MCUA (Uniformly Accelerated Circular Motion): If the instantaneous velocity changes from an initial value (omega initial) to a final value (omega final) in a time interval (increase t), the particle describing the circumference has angular acceleration.
Average Angular Acceleration: Average angular acceleration is defined as the ratio between the variation of the angular velocity and the time elapsed. It’s measured in rad/s2.