In this section, we discuss the various different kinds of mechanical waves: transverse, longitudinal, and some waves which have both of those aspects. Mechanical waves are disturbances which propagate through a medium and transport energy from one region of space to another. In this section, we'll start off with a qualitative description of what mechanical waves.
There are many different ways to describe rotational motion, but the most convenient way of doing so is to replace the role played by the position vector in linear motion with an angular coordinate. This will give us a way of describing the rotational motion of rigid bodies where we do not have to worry about the individual positions of every particle.
Rotational kinetic energy is not a new concept: it is just the sum of all the translational kinetic energies of all the particles comprising a system. Just like how translational kinetic energy is a very important concept in simplifying many problems related to linear motion, the same is true of rotational kinetic energy for rotational motion. Very often, in complicated situations, it is much simpler to use energy concepts than concepts related to force or torque.
We'll see that torque, rotational inertia and rotational acceleration play the same role in rotational mechanics as force, mass, and linear acceleration play in linear motion. Torque is, roughly speaking, how good of a job a given applied force will do at changing the, otherwise, uniform rotational motion; rotational inertia is how much an object resists having its rotational motion changed; and rotational acceleration captures how much the rotational motion is changing from its state of uniform rotational motion. In this section, we'll spend a lot of time focusing on developing a qualitative understanding of torque. We shall also quantify torque and end the section by deriving the rotational analogue of Newton's second law.