Kinetics Click here for a general strategy to solve problems in Kinetics

Key Concepts: A particle has all its mass at one point. So it can only experience translational acceleration. However, a rigid body has distributed mass. Its acceleration includes both translation and rotation. Euler's First Law governs the translational acceleration of a particle or of the center of mass of a rigid body with respect to an "inertial" (fixed-frame) of reference. Euler's Second Law governs the rotational acceleration of a rigid body with respect to an "inertial" (fixed-frame) of reference.

In a Nut Shell: In kinetics you analyze the relationships between the forces acting on a

particle or the forces and moments acting on a body (or interconnected bodies) and the

resulting motion of the particle or of the body (or bodies). Motion (acceleration) can be in a plane or in three-dimensions. The major focus in elementary dynamics is on motion in a plane.

Euler’s 1^st law governs translational or curvilinear motion of a particle or of the center of mass for

a rigid body. The vector form of this law is:

ΣF = m a_c = m dv_c/dt = m a_c

Here ΣF are the external forces acting on the body (determined by a free body diagram), m is its mass, and a_c is the acceleration of its mass center.

In scalar form for plane motion, Euler’s 1^st law takes the following forms:

Coordinate System	Component	Component
Rectangular	Σ Fx = macx	Σ Fy = macy
Intrinsic	Σ Ft = mact	Σ Fn = macn
Polar	Σ Fr = macr	Σ Fθ = macθ

Two classes of problems exist. The first is to determine the acceleration of the center of

mass of the body resulting from the external forces acting on the body. In this type you

must first identify the external forces acting on the body by constructing a “free body diagram”.

The second type is to determine the forces acting on the body resulting from its acceleration.

Also for pure translation of a rigid body there is no rotational (angular) acceleration, so

Σ M_c = 0

Here ΣM_c is the moment of the external forces about C, the center of mass of the body.

Once again you need a FBD to determine the moment of all external forces about the

body’s center of mass.

Click here to continue discussion of kinetics. Click here for an example.

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