Physics final

Issac Newton if you can hear me ...

free fall forces

net force = gravity only, assumed to act at center of mass of the object

if object is spinning about its center of mass in free fall, net torque is zero

to have zero net torque while spinning about center of mass

1. no forces acting on it (deep space) or

2. all external forces act directly through the center of mass

angular momentum of a figure skater

internal forces (any change skater makes to body movements) can’t change total angular momentum of the system

L = I * w → components will change

net torque

If you see an object with a constant shape that is speeding up its spin (positive acceleration), there must be a net torque

If total angular momentum (L = Iw) doesn’t change over time (no external forces), net torque must be zero

kinetic energy in relation to angular momentum and inertia

normal force on a roller coaster loop

normal force doesn’t do work on a roller coaster loop

• instantaneous displacement is perpendicular to normal force = no work

net force if friction force = applied force

net force = 0, so momentum is constant but not necessarily 0

finding net force at a time given velocity and mass functions

multiply functions (foil!), take derivative, plug in time

choosing reference point for computing torque

point where most unknown forces can be named zero

(radius = 0 therefore torque = 0 at that point)

final vs initial angular velocity or rotational inertia (when momentum conserved)

Ii wi = If * wf

simple pendulum equation

ball collision at an angle rules

if initial y momentum is 0, the final y momentum must also be zero

if one ball is at an angle above x axis, other must be at an angle below (one pos sin one neg sin)

ball collision workflow

1. draw a picture (with directions and angles → one pos y one neg y)

2. make equations for x and y components including unknowns (equal masses cancel) m1v1i + m2v2i = m1v1f + m2v2f

3. solve for unknown angle or velocity based on initial y velocity being 0

4. plug unknown into equation to solve

tangent shortcut

tan theta of target object = everything from Y equation/ everything from X equation

use kinematic equations

only when acceleration is constant

when inertia is not constant

need to take derivative of momentum

net torque is derivative of

angular momentum

find net torque from angular acceleration and rotational inertia

angular acceleration α → derivative → angular velocity w → I * w = angular momentum → derivative → net torque

energy formula for rolling without slipping sphere

rolling acceleration formula

• independent of mass and radius

friction on an incline, rolling without slipping

friction at the top of a loop (critical velocity)

• no normal force, so

• no friction

velocity at top of loop (critical speed)

R = radius of loop

height of loop

kinetic energy as a constant

a positive constant for an object falling straight down when its drag euqls its weight, with no other forces acting

work done by friction

minimum speed on a banked curve with friction

ratio of net centripetal force to weight

F = mac, weight = mg

→ ratio = ac/g

pressure

force/area

fluid statics: pressure and depth

perfect (ideal) fluid

• incompressible (constant density)

• non-viscous (frictionless)

• laminar (constant velocity at each point in the fluid)

fluid constants

lift

matter vs energy waves

waves that require a medium (solid, liquid, or gas) = matter

waves that don’t require a medium = energy (electromagnetic, gravitational waves)

transverse waves

medium vibrates perpendicular to the direction the wave is traveling

ex. guitar string vibrations, earthquake s-waves

logitudinal wave

medium vibrates along the same direction the wave is traveling

ex. sound waves in air, p-waves

wave anatomy

frequency

1/period

wave speed

wavelength/period

wavelength * frequency

wave equations

traveling wave

constructive and destructive interference

standing wave anatomy

nodes = locations where the string is held still

antinodes = locations of crests and troughs

1 wavelength = 2 ‘bumps’

• closed ends are displacement nodes

• open ends are displacement antinodes

standing wave harmonics

doppler effect for sound waves

harmonic number

• Open-Open Pipe: Harmonics are 1, 2, 3, 4...(All integers).

• Open-Closed Pipe (Bottle): Harmonics are 1, 3, 5, 7… (Odd only).

• Count the "humps" or loops. If it ends on an open end, you’ll have a ".5" at the end, and you just double it to get the odd harmonic number.

frequency, velocity, length, bump number

4 fundamental forces

gravity, electromagnetic, weak nuclear, strong nuclear

Heat (Q)

thermal radiation

• hotter objects emit light more intensely at shorter wavelengths

total intensity equation

T env = environment temperature in K (= 0 for stars)

e = emissivity of object (0 to1)

internal energy

mechanical equivalent of heat

both heat and work can change internal energy

heat can result in a change in kinetic energy

heat conduction

entropy

an isolated system will always evolve to a state of higher entropy until equilibrium is achieved

(increasing randomness = increasing entropy)

ideal gas law

heat engines

COP of cooling can be bigger than 1

COP heating is 1 more than COP cooling

efficiency can never be more than 1 

carnot cycle

sum of work on a particle

change in kinetic energy