Day 02 - Newton's Laws

Announcements

  • Homework 1 is due next Friday
  • Help sessions will start next week
  • Friday's class will include AI policy discussion
    • We will work Problem 1 together and start discussing Problem 6

Goals for this week

Be able to answer the following questions.

  • What is Classical Mechanics?
  • How can we formulate it?
  • What are the essential physics models for single particles?
  • What mathematics do we need to get started?


Take 2 min to write down what comes to mind when asked:


What is "Classical" Physics?

Classical Mechanics

Modeling large, slow-moving objects

Newton's Laws are but one of a number of formulations:

  • Lagrangian Mechanics
  • Hamiltonian Mechanics
  • Dynamical Systems Theory
  • ...

An Overview of Different Physics

Classical Mechanics is still very relevant

Tiny Limbs and Long Bodies: Coordinating Lizard Locomotion
Research Lab

Tiny Limbs and Long Bodies: Coordinating Lizard Locomotion
Source: https://youtu.be/Qme07fA3Fj4

Think-Pair-Share

We used a tilted coordinate system ( plane) to analyze the motion of a block on an inclined plane. How can we check that we did the gravitational force decomposition correctly?

Recall:

Come up with at least two checks.

Clicker Question 2-1

The formal definition of a Taylor series expansion around a point is:

This formula makes me feel:

  1. Confident, I got this.
  2. A little nervous, but I think I remember.
  3. Uncomfortable, I don't remember this.
  4. I have no idea what this is.

Think-Pair-Share

We derived the following differential equation for the falling ball in one-dimension:

Let's assume the turbulent drag term is negligible. Is there an anti-derivative of the right-hand side of this equation? If so, what is it?