Principles of Dairy Machine Design

Module 2. Dynamics

Lesson 6
DYNAMICS

6.1 Introduction

In the field of physics, the study of the causes of motion and changes in motion is dynamics. In other words the study of forces and why objects are in motion. Dynamics includes the study of the effect of torques on rotating components. These are in contrast to Kinematics, the branch of classical mechanics that describes the motion of objects without consideration of the causes leading to the motion.

6.2 Rigid Body

A body is said to be rigid, if the relative positions of any two particles in it do not change under the action of the forces. In Fig. 6.1 (a) points A and B are the original position in a body.

After application of a system of forces F1, F2, F3, the body takes the position as shown in Fig. (a,b)A¹ and B¹ are the new positions of A and B. If the body is treated as rigid, the relative position of A¹B¹ and AB are the same i.e.

A¹B¹ = AB.

Fig. 6.1 Rigid body

6.3 Translation

Orientation of the body never changes. Every line segment on the body remains parallel to its original direction.

1. The movements of the points in a rigid body are parallel.
2. Every point has same velocity and acceleration
3. Motion of one point completely describes the motion of the entire rigid body. We generally choose the motion of the center of mass to denote the motion of the rigid body.

Fig. 6.2 Translation

6.4 Pure Rotation

The rigid body rotates about a fixed axis

1. All points are rotating about same fixed axis.
2. No two points have same linear velocity or linear acceleration although all of They have same angular velocity and angular acceleration.

Fig. 6.3 Pure rotation