Physics 131 Lecture Notes

Ohio State University Marion Campus

by Gordon Aubrecht

©copyright 1998-2003 all rights reserved

These notes sketch the topics that will be the focus of each class. You may use them to refresh your mind, and to help you structure your "lecture" notes.

Class 1

Introduction--describe Physics 131

How the days are structured; what is expected.

Grading policy explained (syllabus on paper & web)

"Gordon's forgiveness policy"

Choice for exams:

a) Small number of questions, if you miss one it can cause a big problem with your grade but mean grade is higher.

b) Large number of questions; but then low midterm and final mean grades.

Introduction to the Physical World

The particle model and other models used in physics--utility, limitations.

What is science?

• skeptical
• taxonomic
• falsifiable
• experimental
• willingness to accept no for an answer
• reductionist

Experiment as the bellwether.

What is physics? Excitement!

What are physics's limits?

Class 2

Newton's First Law:

Unbalanced forces result in a change in the motion.

Forces all act on one body.

the newton

contact vs. noncontact forces

Examples of forces in everyday life.

Simplification of the world:

• objects are point particles
• ideal ropes
• massless ropes
• massless, frictionless pulleys
• walls, supports "ideal"
• frictionless surfaces
• neglect of air resistance and drag
• point objects
• charges of no spatial extent
• test charges that have no effect of the region around them
• and so many more ...

Class 3

Forces in Nature

• strong
• electromagnetic
• weak
• gravitational

Electromagnetic plus weak becomes electroweak.

Electroweak plus strong becomes GUT (grand unified theory).

GUT plus gravitation becomes supersymmetry? the theory of everything? ??

force vs. impulse

vectors vs. scalars

weight--a vector force

surfaces exert forces on objects or bodies that touch them

free body diagrams (FBDs) and point masses

Class 4

Vectors

trigonometry

components

reference frame/coordinate system

addition

• tip-to-tail method
• component method: i-hat, j-hat, k-hat
• ordered pair method

subtraction

length

meaning

Compare two and three dimensions to one dimension

Class 5

Equilibrium and Newton's Third Law

Newton's Third Law:

Do Newton's Third Law examples and problems

Pairs act on different bodies.

Equilibrium:

The sum of the forces acting on a body is zero.

This is a vector relation.

Do examples.

Free Body Diagrams in detail

The force diagram compared to the free body diagram.

Identify THE body.

DRAW THE DIAGRAM!

Note that Newton's Third Law refers to two different bodies: If A exerts a force on B, B exerts an equal and oppositely directed force on A.

Do examples showing how these ideas are used.

Ropes transmit forces.

Class 6

Inertia--Operational Definition of mass

What does mass do?

Friction

static (no motion) friction: the force of static friction is just such that no motion occurs up until some maximum force is attained.

kinetic friction: bodies are moving relative to one another

Model: find force with which surfaces push together; then the frictional force is proportional to that force. The constant of proportionality is called the coefficient of kinetic friction.

The "normal" force; inclined planes

Show how to work problems--putting it all together.

Class 7

Newton's Second Law

Acceleration measures the change in motion of the object.

Newton's Seccond Law: F = ma

do examples of how to use Newton's Second Law

• masses touching
• elevator

Weight is a force

W = mg

Class 8

Coordinate systems and their consequences

What is a coordinate system?

Components.

Distance: s

Displacement: r

Motion means change.

Intuition about speed.

What (average) speed is.

v_average = (change in s)/(time interval involved)

The difference between speed and velocity (v and v).

v_average = (change in r)/(time interval involved)

Instantaneous speed and velocity compared to average speed and velocity.

The m/s, the km/h.

Class 9

Defining acceleration

Acceleration means any of: increasing speed in the direction of motion, decreasing speed in the direction of motion, changing the direction of motion.

a_average = (change in v)/(time interval involved)

Using average acceleration to solve for v(t); v(t) = v₀ = a_average t.

Applying this to a baseball's trajectory, Big Bertha (range 122 km), etc.

Class 10

More "realistic" motion: using finite differences

Air resistance or drag models:

• F = -kappa v
• F = k v²

Explain without air resistance

Explain how to model air resistance

Class 11

Finite differences

What does "finite difference" mean?

Using a spreadsheet to calculate (write the "program" in class).

Class 12

Reference frames

Galilean relativity

v_{1-compared-to-3} = v_{1-compared-to-2} + v_{2-compared-to-3}

Do examples.

Why would anyone think there's a need to change: Fizz as observer vs. Tre'nbeth in the rocket ship as observer.

The interval as an invariant between reference frames.

The scalar product.

Class 13

Circular Motion

r(t) = R (cos(theta) i-hat + sin(theta) j-hat)

How do we get v(t)?

How do we get a(t)?

Define average angular velocity: .

omega_average = (change in theta)/(time interval involved)

Relation between v and R.

Relation between a and v.

Class 14

Momentum

p = gamma mv

gamma = sqrt(1 - v²/c²), approximately 1 at low speed

F = dp/dt.

Class 15

Momentum

Center of mass. The V_CM and A_CM.

Newton's Third Law

Is approximation that object is a point so bad after all?

Impulse is change in momentum over the time--integral of F dt.

Class 16

Momentum Conservation

Conservation Laws and symmetry

Noether's theorem

Momentum conservation in particle decays: neutron decay into proton.

Inferring the neutrino.

Class 17

Momentum Conservation

Examples of momentum conservation.

Inelastic collisions.

Class 18

Work

motivation

work done = F (dot) displacement [only if F is constant]

The integral method

the joule

work done against gravity: Wh = mgh

Internal work

Class 19

Energy and Power

kinetic energy

gravitational potential energy

spring potential energy

power: P = dW/dt.

the watt

Class 20

Conservation of Energy

Mechanical energy

bar diagrams

Conservation of energy in a closed system (the universe or a subsystem)

Noether's theorem

Machines

• amplify force
• do not create mechanical energy

Ideal machines: (force)_IN(distance)_IN = F_OUT d_OUT

Real machines: W_OUT < W_IN

distortion (elasticity), thermal energy, etc.

Class 21

Thermal Energy, Relativistic Energy, Elastic Collisions

purely elastic collisions

Thermal energy

Relativistic energy (mass energy)

E² = p² c² + m² c⁴

becomes

(massless) pc

(massive) gamma m c²

Class 22

Simple Harmonic Motion

demonstration

springs and Hooke's Law

phase diagrams

Equation for SHM for a spring

Equation for SHM for a simple pendulum

cycle

y(t) = A cos (omega t + delta)

period, T

frequency, f

amplitude, A

damped harmonic oscillation

Class 23

Waves

pulse vs. wave

both carry momentum and energy

amplitude and wavelength

transverse vs. longitudinal waves

wave speed: c = f (wavelength) = fl

y(x) = A cos (k x + d-prime)

k = 2 p/l

traveling waves

psi(x,t) = A cos (w t +/- k x + d)

transverse speed; partial derivative

transverse acceleration; partial derivative

the wave equation

dispersion of waves