Kinematics and Dynamics of Motion

Kinematics and Dynamics

Kinematics studies movement irrespective of its causes, while dynamics analyzes the causes of motion.

Types of Motion

Translational Motion

Occurs when all points of a body change position.

Rotational Motion

Occurs when a body rotates around a fixed axis; it moves but doesn't travel linearly.

Inertial Reference System

A system where the reference point (0) is at rest or moving at a constant velocity. Earth can be approximated as an inertial reference point, despite its rotation, as this motion is imperceptible to us.

Motion Concepts

Path

The trajectory of successive positions a moving point occupies in space.

Position Vector

A vector originating from the coordinate system's origin, ending at the mobile's current position.

Displacement Vector

Calculated by subtracting the initial position vector from the final position vector.

Distance Traveled

The total length of the path followed by the mobile. It equals the displacement magnitude only in straight-line motion without direction changes.

Average Speed

The displacement of the moving point per unit of time. It's a vector obtained by dividing the displacement by the time interval. Its direction is the same as the displacement vector, as time is a positive scalar. V = Δr / Δt

Instantaneous Velocity

The velocity of a particle at a specific time or point on its trajectory. It's a vector whose magnitude is called speed, and its direction is tangent to the path.

Acceleration

The rate of change of velocity over time.

Average Acceleration

The vector resulting from dividing the change in velocity by the time interval.

Instantaneous Acceleration

The limit of average acceleration as the time interval approaches zero. It's the derivative of the velocity vector with respect to time.

Tangential and Normal Acceleration

Tangential acceleration is due to changes in speed (magnitude of velocity). Normal (centripetal) acceleration is due to changes in velocity's direction. Its magnitude is v²/R, where v is speed and R is the curve's radius.

Angular Velocity (ω)

Defined as the angle rotated by the position vector per unit of time.

Frequency (f)

The number of revolutions per second. Period (T) and frequency are reciprocals: T * f = 1.

Average Angular Acceleration

The ratio of the change in angular velocity to time. Measured in rad/s².

Free Fall

The motion of a body under gravity's influence. It's a uniformly accelerated vertical motion.

Superposition Principle

If a particle experiences multiple independent elementary movements simultaneously, the resulting motion is the vector sum of these partial movements.