Lesson 6:
The Big Mo, Force and Momentum

6. Lesson 6:
The Big Mo, Force and Momentum#

We’re all about modern particle physics and the collisions we create in order to see into the deepest depths of reality. But in order to get there we need forces to accelerate our beams to high momenta and a language to describe their energies. In addition, we learned long ago that the most intriguing feature of the particles we produce is: mass. All of these concepts have their roots in Newton’s notebooks: Force, acceleration, momentum, and mass.

But even though our subject is very contemporary, we’re stuck with the definitions and terminology from the 1600’s, when our heroes emerged: Galileo, Kepler, Descartes, Huygens, Leibnitz, and Newton. While some of those fellows are important for their brilliant intuition (Galileo, Kepler, Descartes), only Isaac Newton, Gottfried Leibnitz and Christiaan Huygens wrote down mathematical relations which form the language, and, yes, the metaphors of our modern models of how things move. Typically, we divide mechanics into two parts:

Kinematics is the description of the motion of objects without regard to what caused them to move. If a ball is accelerating by some amount, the rules of kinematics will tell you how far it will go in a given time, how fast it’s going after a given distance: time, distance, speed, and acceleration are the parameters of kinematics. When you estimate how long it will take you to arrive at a destination, you’re doing kinematics. We tend to attribute the important ideas of kinematics to Galileo, but he didn’t have algebra and the actual mathematics of the kinematical rules came later with Newton and others. What we did in the lesson on Galileo and motion is sufficient for our purposes.

Dynamics is the study of forces—their causes and their consequences. According to Newton, forces create accelerations in objects by pushing or pulling. That’s how the ball in the previous paragraph got its acceleration—something pushed on it. This is a big subject, but we will only consider motions in one dimension, except for circular motion.

  Goals of this lesson:

Understanding, Appreciation, and Familiarity

I’d like you to Understand:

  • How to calculate a force required to produce a particular acceleration in one dimension.

  • How to calculate the average change in momentum induced by the application of a force through a finite period of time.

  • How to calculate the centripetal force and acceleration for an object moving at a constant, circular speed.

I’d like you to Appreciate:

  • Forces create accelerations.

  • That if a momentum vector is changing in direction or magnitude, a force is the cause.

  • That an object moving in a curved path must have had a force applied to it perpendicular to the trajectory.

I’d like you to become Familiar With:

  • Newton’s third law

  • Newton’s Life