KEY FEATURES

The key concepts in this chapter are the velocity and acceleration of a particle and the angular velocity of a rigid body in planar motion.

Kinematics is the study of the motion of material bodies without regard to the forces that cause their motion. The subject does not seek to answer the question of why bodies move as they do; that is the province of dynamics. It merely provides a geometrical description of the possible motions. The basic building block for bodies in mechanics is the particle, an idealised body that occupies only a single point of space. The important kinematical quantities in the motion of a particle are its velocity and acceleration. We begin with the simple case of straight line particle motion, where velocity and acceleration are scalars, and then progress to three-dimensional motion, where velocity and acceleration are vectors.

The other important idealisation that we consider is the rigid body, which we regard as a collection of particles linked by a light rigid framework. The important kinematical quantity in the motion of a rigid body is its angular velocity. In this chapter, we consider only those rigid body motions that are essentially two-dimensional, so that angular velocity is a scalar quantity. The general three-dimensional case is treated in Chapter 16.

STRAIGHT LINE MOTION OF A PARTICLE

Consider a particle P moving along the x-axis so that its displacement x from the origin O is a known function of the time t.