Kinetic Analysis

D’Alembert’s principle

By this principle, a particle or a system of particles moving with a constant acceleration is known as in dynamic equilibrium.

For a particle

Here:

• - resultant applied force
• - mass of the particle
• - acceleration of the particle

is known as the inertia force which is fictious.

For a system of particles

The equation can be rewritten as:

Here:

• - resultant applied force
• - mass of a particle
• - acceleration of a particle
• - total mass
• - acceleration of the center of mass

Kinetics of a Rigid Body

Both translational and rotational aspects of the motion must be considered.

Here:

• - resultant applied force
• - mass of the body
• - acceleration of the body
• - moment of the resultant force
• - mass moment of inertia
• - angular acceleration of the body

General plane motion

Here:

• - moment about center of mass
• - mass moment of inertia about center of mass
• - angular acceleration of the body

Let be a point other than .

Kinetic energy

Center of percussion

The point on an object attached to a pivot where a perpendicular impact will produce no reactive shock at the pivot.

Translational and rotational motions cancel at the pivot when an impulsive blow is struck at the center of percussion.

Here:

• - Center of percussion
• - Center of gravity
• - Pivot

For a uniform rod: