Understanding Fundamental Motion Principles in Physics

Uniform Rectilinear Motion (MRU)

An object performs Uniform Rectilinear Motion (MRU) if it travels equal distances in equal times and its trajectory is a straight line. The equation of motion allows us to determine the position of the body at every moment.

Uniformly Accelerated Rectilinear Motion (MRUA)

An object experiences Uniformly Accelerated Rectilinear Motion (MRUA) if its velocity changes by equal amounts in equal times, and its trajectory is a straight line.

Circular Motion (MC)

Circular Motion (MC) describes the path of an object along a circumference. For its study, the center of the circle is typically placed at the origin of the coordinate system. The following characteristics are always fulfilled:

• The magnitude of the position vector r is always equal to the radius R of the circle: |r| = R.
• The velocity vector v is always perpendicular to the position vector r.
• The trajectory of the object is a circular arc.

Angular velocity (ω) is defined as the angle rotated by the position vector per unit time, expressed in radians per second (rad/s). Linear displacement and linear velocity are obtained by multiplying the respective angular magnitudes by the radius.

Uniform Circular Motion (MCU)

Uniform Circular Motion (MCU) is performed with constant angular velocity. In this case, the average angular velocity coincides with the instantaneous angular velocity. Solving the relevant equations yields the equations of motion.

MCU is often defined by the following magnitudes:

• Period (T): The time it takes for the object to complete one full revolution (2π radians), measured in seconds.
• Frequency (f): The number of revolutions the object makes per second, calculated as the inverse of the period (f = 1/T).

Uniformly Accelerated Circular Motion (MCUA)

When in circular motion, the angular velocity undergoes changes, we define a new magnitude: average angular acceleration. This is the variation of angular velocity per unit time, expressed in rad/s². An object performs Uniformly Accelerated Circular Motion (MCUA) if it moves with a constant angular acceleration. The angular velocity (ω) at any moment is obtained by solving the relevant equation. The angular displacement in MCUA is obtained using specific formulas. Linear velocity can be determined from the angular velocity and radius.

Composition of Motion

If an object is subjected simultaneously to two or more movements, their resultant kinematic quantities are obtained by adding the kinematic quantities of the different movements. If an object is subject to two movements, the change in position is independent of the order in which the movements act simultaneously or successively.

Composition of Perpendicular Rectilinear Motions

Consider an object simultaneously undergoing uniform rectilinear motion in the x-direction with equation x = x₀ + vₓt, and a uniform rectilinear motion in the y-direction with equation y = y₀ + vᵧt. The composition of these two movements results in another movement where the position of the object is calculated using a vector sum:

r = xi + yj = (x₀i + y₀j) + (vₓi + vᵧj)t

The resultant velocity is constant:

v = vₓi + vᵧj

Its direction is given by the angle α where tan(α) = vᵧ / vₓ. The equation of the trajectory is:

(y - y₀) = (vᵧ / vₓ)(x - x₀)

The composition of two perpendicular Uniform Rectilinear Motions results in another Uniform Rectilinear Motion.