This lecture covers the concept of cutting speeds, including cutting speed, shearing speed, friction speed, and material removal rate. It explains the three main speeds involved in cutting processes: cutting speed, material movement speed, and tool advancement speed. The relationships between these speeds are trigonometrically related, impacting the cutting process. The lecture also delves into calculating material removal rates and volumes, considering the relationship between tool advancement and material removal. It concludes by discussing the dilation rate of the material during cutting, showing that the cutting process does not significantly alter the material volume due to the nature of shear operations.