**Branch :**First Year-Engineering Syllabus

**Subject :**Elements of Mechanical Engineering

## Kinetics of body

**Kinetics of body:**** Translation: In rigid body** translation in plane motion, every line in a translating body remains parallel to its original position at all times. In rectilinear translations all points move in straight lines, whereas in curvilinear translation all points move on congruent curved paths

rectilinear translation.

curvilinear translation.

For both the translations, and .

Therefore for translational body,

**Fixed-Axis Rotation:**

Let us consider a noncentroidal rotation. It is a motion, in which, the rigid body is constrained to rotate about fixed axis, not passing through its mass center. For a rigid body rotating about a fixed axis *O*, all points in the body describe circles about the rotation axis, and all lines of the body in the plane of motion have the same angular velocity and angular acceleration *a*. The normal acceleration is .

Equations of dynamics are:

Thus,

and

In applying the moment equation about *G*, it is essential to account for the moment of the force applied to the body at *O*, so this force must not be omitted from the freebody diagram.

Consider the free body diagram of the body. The corresponding kinetic diagram is also shown

We know that,

Thus.

However *O* is fixed, thus ;

For the common case of rotation of a rigid body about a fixed axis through its mass center *G*, clearly *a* = 0, and therefore . The resultant of the applied forces then is the couple .