Principles of Uniform Circular Motion and Dynamics

Uniform Circular Motion

There are many everyday movements that are familiar and not rectilinear. We focus here on circular motion.

Arc and Angle

In circular motion, a mobile object covers an arc of the trajectory while simultaneously traveling through an angle. The radian is the value of the central angle that subtends an arc whose length is equal to the radius.

Angular Velocity

This is the relationship between the angle turned and the time spent; this magnitude is similar to the speed of rectilinear movement.

Angular Acceleration

This is the relationship between the variation of angular velocity and the time spent to effect it.

Normal or Centripetal Acceleration

This vector may be constant in magnitude but not in direction. It is perpendicular to the linear velocity and is always directed toward the center of rotation in uniform circular motion.

Period and Frequency

• Period: The time it takes for an object to complete a full turn.
• Frequency: The number of turns an object completes per unit of time.

Force and Dynamics

Force is any influence that can deform a body or change its state of rest or motion.

Deformations

Plastic deformations occur in bodies, such as clay, that cannot recover their original shape when the force stops acting.

Moment and Torque

• Moment of a Force: A vector quantity resulting from the product of the force value and its distance from the reference point.
• Torque: A system of two parallel forces equal in magnitude and opposite in direction, but not sharing the same point of application, which causes a body to rotate.

Newton's Laws of Motion

1. First Law: A body remains in its state of rest or uniform rectilinear motion unless acted upon by external forces.
2. Second Law: Bodies undergo changes in speed when forces act upon them. The change of motion is directly proportional to the force and inversely proportional to the mass.
3. Third Law: If a body exerts a force on another (action), the second body exerts a force of the same intensity and direction but opposite sense on the first (reaction).