Understanding Forces and Motion: Dynamics Principles

Posted on Apr 6, 2025 in Physics

Forces and Motion

Forces: They are interactions between bodies that can produce motion or deformation. Forces are measured with a dynamometer, and their SI unit is the newton (N). Forces can be contact forces, such as friction, or act remotely, such as weight. They are represented by vectors.

Identifying Forces in Motion

Whenever there is a change in the velocity vector (V), the object will be accelerated, and therefore, there is a resultant force. This occurs in the following cases:

  • Movements with curved trajectories, where the velocity direction changes.
  • Movements with a curved distance-time (St) graph, where the magnitude of the velocity changes.
  • Movements with a velocity-time (Vt) graph that is not a horizontal line, indicating that the speed is changing.

Principles of Dynamics

First Principle of Dynamics

A body on which there is no resultant force does not change its speed. If at rest, it remains at rest; if in motion, it remains in uniform rectilinear motion.

Second Law of Dynamics

The resultant force on a body is proportional to the acceleration it produces: F = ma. The constant of proportionality is called inertial mass.

Third Principle of Dynamics

When a body exerts a force F12 on another, the second body exerts an equal and opposite force F21: F12 = -F21. These forces are called action and reaction and do not cancel each other out because they act on different bodies.

Effects of Forces on Initial Velocity

If the force is parallel to the velocity, it varies the magnitude of v:

  • Increases if the force has the same direction as v.
  • Decreases if the force has the opposite direction to v.

If the force is perpendicular to the velocity, it changes its direction without changing its magnitude.

If the force is neither parallel nor perpendicular to the speed, it varies both the magnitude and direction of v.

Forces on Solids

A deformable solid changes shape when a force is applied to it. A rigid solid does not change its shape when a force is applied.

Forces on rigid bodies can cause translation or rotation. The effects of translation and rotation depend on where the force is applied on the solid.

The Moment of a Force

The moment of a force measures its capacity to produce rotation. Its value is the product of the force’s magnitude and the distance between the axis of rotation and the line of action of the force.

M = F * d

In the International System of Units, the unit for the moment is the newton-meter (Nm).

Composition of Parallel Forces

The sum of two parallel forces F1 and F2 in the same direction, applied at points O1 and O2, respectively, is a force that:

  • Has the same direction as the components.
  • Its magnitude is R = F1 + F2.
  • Its point of application satisfies the ratio F1 * d1 = F2 * d2.

Torque

Torque is a system of two parallel forces equal in magnitude and opposite in direction. The moment of a torque is the product of the magnitude of one of the forces by the distance between the lines of action of the forces:

M = F * d

Static Equilibrium

The conditions necessary for a rigid body to remain in static equilibrium are:

  • The resultant of the forces acting on the solid must be zero.

R = 0

  • The net moment due to the forces acting on the solid must be zero.

M = 0

Center of Gravity

The center of gravity of a solid is an imaginary point, G, where the body’s weight is considered to act.

A solid is in equilibrium when the vertical line through its center of gravity falls within its base of support.

Equilibrium in Simple Machines

The lever, pulley, inclined plane, and screw are simple machines.

The Lever

The lever is a rigid bar with a fulcrum. The product of the effort and its distance from the fulcrum equals the product of the resistance and its distance from the fulcrum (law of the lever).

P * bP = R * bR

The Pulley

The pulley can change the direction of a force. In fixed pulleys, the effort is equal to the resistance.

P = R