Energy and Momentum Concepts – Week 2 Lecture

Instructor is recording a lecture and aims to cover a lot of information without staying up too late; planning to keep it under nine by starting early and avoiding rushing.
Uses online simulations from the University of Colorado Boulder (locally hosted) as visual aids for concepts in physics, chemistry, and math; emphasizes their value for remote learning.
Week 2 focus: energy (me mechanical energy, and a bit of pressure and atomic structure), and heat; Week 3 will be a relatively short lecture on waves and sounds.
The course is relevant to diagnostic medical sonography (DMV) students, so waves and sounds are particularly important for many students.
The instructor plans to explore a one-dimensional (1D) collision simulation this week rather than two-dimensional collisions.
Introduction to a visual example: an anime character holding a ball of energy to illustrate the concept of energy (a simplified metaphor).

Energy is something that can transform from one form to another; energy cannot be literally held in your hands.
The instructor emphasizes a distinction between different kinds of energy:
- Mechanical energy: the energy associated with objects that are moving (kinetic energy) or objects at rest/other configurations (potential energy in a broader sense).
- General concept of energy: broadly, energy describes the capacity to do work or cause change; energy can move or transform but is not a tangible object to be held.
A common-sense, though imperfect, statement shown: “Energy is light”. The speaker notes energy is associated with anything that moves at the speed of light, and light carries energy. This is a conceptual analogy rather than a strict definition.
Energy transformations are central: energy can move through systems and transform between forms, but the total amount can be conserved under certain conditions.
The visualization uses a ball of energy in the simulation to hint at energy transfer during interactions, though the speaker acknowledges the physical impossibility of literally holding energy.

Conservation of energy:
- If you start with a certain amount of energy, you end with the same amount after interactions (ignoring external work/heat exchange, etc.).
- Mass-energy equivalence provides a link: E = m c^2, meaning a small amount of mass can correspond to a large amount of energy. This is most noticeable in stellar cores (e.g., in stars), not in everyday human experiences.
Conservation of momentum:
- Momentum is a conserved quantity in interactions where external forces are negligible (an isolated system).
- Momentum is not an energy, and it is not a force; it is mass times velocity (vector): p = m v.
- Momentum can be converted or redistributed in interactions, but the total momentum before an interaction equals the total momentum after (in the absence of external impulses).
Note on the relationship between energy, momentum, and force:
- Momentum is not a form of energy and is not itself a force.
- A force acting over time (impulse) changes momentum: ext{Impulse} = F imes ext{time} = riangle p.

Definition: Momentum is the product of mass and velocity; it includes both magnitude and direction: p = m v.
Momentum as a conserved quantity: In closed systems with no external forces, total momentum is conserved before and after interactions.
The speaker uses a 1D collision simulation with two objects (teal and magenta balls) to illustrate momentum concepts:
- Teal ball: mass = 0.5 ext{ kg}, velocity = 1 ext{ m s}^{-1}
- Magenta ball: mass = 1.5 ext{ kg}, velocity = -0.5 ext{ m s}^{-1} (negative indicates the opposite direction).
Focus of the visualization:
- Emphasizes that the quantities to track are mass and velocity (not the position).
- Example momenta:
- Teal: p_{ ext{teal}} = (0.5 ext{ kg})(1 ext{ m s}^{-1}) = 0.5 ext{ kg·m s}^{-1}
- Magenta: p_{ ext{magenta}} = (1.5 ext{ kg})(-0.5 ext{ m s}^{-1}) = -0.75 ext{ kg·m s}^{-1}
- Total momentum in this snapshot: p{ ext{total}} = p{ ext{teal}} + p_{ ext{magenta}} = 0.5 - 0.75 = -0.25 ext{ kg·m s}^{-1}
The simulation illustrates how momentum is distributed between objects, and sets up the context for momentum conservation in interactions.

Energy units:
- The unit of energy is the joule: ext{J}, where 1 ext{ J} = 1 ext{ N·m} = 1 ext{ kg·m}^2/ ext{s}^2.
Force units:
- The unit of force is the newton: ext{N} = ext{kg·m}/ ext{s}^2.
Momentum units:
- Momentum units are ext{kg·m}/ ext{s} (not Newton seconds in general). The impulse unit is ext{N·s}, which equals the change in momentum riangle p = J.
The speaker notes a common confusion: a newton-second (N·s) is not the unit for momentum itself; it is the unit for impulse, which equals the change in momentum.
The speed of light is a central constant in mass-energy relation, typically denoted $$c \