Calculus Physics I
Equation Sheet for Exam III
Circles
2 - 1
ave / t
d /dt
and
sr
ave / t
v=r
and d /dt = d2 /dt2
atang = r
arad = r 2 (centripetal)
constant
(t) = o + o t + t2
(t) = o + t
2 = o2 + 2 ( o )
dI r2 dm
or
I=
i
mi ri2
or
I=
r
2
I| = ICM
Newtons laws applied to circular motion
Case one: Uniform circular motion [UCM]
To the ancient Greeks, uniform circular motion was considered the only
perfect form of motion. Today we study perfection!
In this case the particle moves in a circle of radius
Newtons laws of motion
THEORY
Isaac Newton formulated his three laws of motion in the 1600s. These form
the foundation for understanding motion in the everyday world. Two new
concepts appear: force and mass.
Definitions
Force a push or a pull, measured i
Potential energy and conservation of energy
THIS LECTURE IS ONE OF THE MOST IMPORTANT OF THE
SEMESTER!
Potential Energy
We have seen that when a force does work on a system the system
may acquire motion energy, i.e. kinetic energy. However, another
possib
Rotational energy and mass
Consider a rigid body rotating about a fixed axis of rotation. The
kinetic energy is by definition,
K i mi vi2 .
But we have already noted that the speed of the ith particle may be
written in terms of the angular velocity of the
Rolling motion, angular momentum vector and cross products
Now, for the physics version of Nascar racing. The entries in this
marathon are: a particle, hoop, cylinder, and sphere. These objects
are to race down an inclined plane. Neglecting friction, mech
Rotational dynamics
The effect of a force is to produce an acceleration of the object the
force acts on.
What causes an angular acceleration? This comes about by action
of a force in causing a twisting motion of that it acts on. The
twisting action of a f
Rotational kinematics
Rotational kinematics involves six definitions, here we go again.
time, t
time interval,
angular position,
angular displacement,
angular velocity,
angular acceleration,
t tf - ti
f - i
d /dt
d /dt
Note: in going from linea
Second law of thermodynamics &
heat engines
Some processes one might imagine obey the first law of
thermodynamics but still do not happen. For example, heat
flows spontaneously from hot to cold but not from cold to
hot even though this would conserve ener
Simple Harmonic Motion
THEORY
Vibration is the motion of an object back and forth over the same ground.
The most important example of vibration is simple harmonic motion (SHM).
One system that manifests SHM is a mass, m, attached to a spring where k is
th
Linear momentum and the impulse-momentum
theorem
Definition of linear momentum of a particle
Consider a system of N particles, each with a position vector, ri .
The ith particle has mass mi and velocity, vi . We define the linear
momentum of the particle
Kinetic Theory of Ideal Gases
THEORY
An ideal gas consists of atoms that do not exert forces on each other and
collide with the walls of the container in elastic collisions. The atoms obey
the ideal gas law:
PV = nRT,
where R is the universal gas constant
Introduction
to
Thermodynamics;
Temperature and Its Effects; Ideal Gas Law
Introduction to thermodynamics
The standard model in thermodynamics is a cylinder with a
piston and an ideal gas inside.
Thermodynamics divides the world into a system (e.g. the
id
Calculus Physics I
Equation Sheet for Exam IV
F = -k x
x(t) = A cos( t + )
E = kA2
T = 2 (L/g)
y = y(x,t)
f
v = (FT/ )
= (k/m)
y(x,t) = A sin(kx - t)
k = 2 /
Pave = 2 A2 v
= 2 f
= 2 f
f = 1/T
f = 1/T
v=
vy = y/t
sin + sin = 2 cos[( - )/2] sin[( + )/2]
Calculus Physics I Equation Sheet V
C Q/ T
|Qloss| = |Qgain|
Eint = Qin Wout
c (1/m) Q/ T
c (1/n) Q/ T
or
L Q/m
n N/NA = m/M
R=NAkB
Eint = f kBT
Vf
W = P dV
Vi
PV = nRT
Eint = n cv T
Wout/QH = 1 QC/QH
S = dQrev/T
cP = cv + R
cP/cV
C = 1 TC/TH
Sisol
Specific heat of ideal gases and the
equipartition theorem
Specific heats revisited
The specific heat of a material will be different depending
on whether the measurement is made at constant volume or
constant pressure.
Molar specific heat at constant vo
PHY 2048 Calculus Physics I
Fall 2006 Section 80182 Four Semester Hours 50/1102
Tuesday & Thursday 9:25 AM 10:40 PM, Friday 12 12:50 PM
Course Website: http:/www.unf.edu/coas/chemphys/phys/physics.html
This course is the first physics course for students
Phase Transitions; First Law of
Thermodynamics
Phase Transitions
All of us are aware of the three states (or phases) of matter: solid
(S), liquid (L) and gas (G). There are other, less common, states of
matter: superconductor, superfluid, and ferromagnet
Gravitational force and field
THEORY
In the seventeenth century Isaac Newton proposed the universal law of
gravitation, which states the gravitational force one point mass, M, exerts
on another point mass, m, when the two are separated by a distance, r, h
Gravitational Potential Energy
THEORY
Recall the change in potential energy of a system, V, is related to the work,
W, by the force one part of the system exerts on the other,
U - W = Wext
where Wext is the work by an external force against the gravity f
Thermal Expansion and Heat Transfer
Thermal Expansion
A rod of length L will expand by L when its temperature
increases by T. It is found L is proportional to T,
L = L T,
where is the one dimensional thermal expansion coefficient.
These coefficients appe
INTRODUCTION TO CALCULUS PHYSICS I
Welcome to first semester physics with calculus.
Below are a few suggestions and topics to study that we wont be covering
in class.
Buy the cheapest solar-powered scientific calculator available.
Systems of units
MKS,
Internal Energy Eint , Heat Q, and Specific
Heat c
From mechanics we found energy comes to us in various
forms: kinetic energy associated with translational and
rotational motion and potential energies associated with
various conservative forces.
In therm
Dynamics of a N-particle system
Consider a system of N particles. The mass of this system may be
written,
M
i
mi ,
where the sum on i runs from i = 1 to i = N.
For this system we define a new vector called the center of mass
position vector,
R (1/M) i mir
Standing Waves
Lab #12
December 3rd 2014
Prachee Patel
Morsal Osmani and Megan Burrett.
Summary:
In physics, a standing wave is also known as a stationary wave. This is a wave
that remains in a constant position over a certain amount of time. This only oc
Torques and Rotational
Equilibrium!
Lab #9
October 23rd 2014
Prachee Patel
Morsal Osmani and Megan Burrett.
Summary:
When the ability of a force that allows rotating an object about a fixed axis is
measured by a quantity of torque. A torque can be thought
Residuals
The difference between the observed value of the dependent variable (y) and the predicted value
() is called the residual (e). Each data point has one residual.
Residual = Observed value - Predicted value
e=y-
Both the sum and the mean of the re
Free Fall and Acceleration Due to Gravity
Lab # 3- January 26, 2017
Jenny Herard, Group #7
In lab 2, Free Fall and the Acceleration Due to Gravity, we learn near the surface of the Earth where an
objects distance from the center of the Earth does not chan
Distance (mm)
(a)
(b)
(c )
(d)
(e )
(f)
Average
Percent Error
Std Deviation
Std Error
Mean
Std Deviation (SN-1)
Std Error (Semean)
Sue's Average Value
(g)
Joe's Average Value
(h)
Ann's Average Value
(i)
(j)
(k)
Sue
229.7
228.0
231.2
230.5
229.4
229.8
4.4
Conservation of Energy, and Newtons Law
Lab # 6- Feb 16, 2017
Jenny Herard, Group #7
This week we have enough of the basic concepts to begin a discussion of energy itself.
Energy is sometimes introduced as if it is a concept independent of Newtons laws (t
Newtons 2nd Law and Circular Motion of Pendulum
Lab # 5- Feb 9, 2017
Jenny Herard, Group #7
Newtons second law of motion pertains to a specific behavior of objects for which all of
the forces acting on an object is not balanced. The second law states that
Composition and Resolution of Concurrent Forces
Lab # 4- Feb 2, 2017
Jenny Herard, Group #7
In Lab 4, the Composition of Resolution of Concurrent Forces, we learned about physical
quantities that are used in Physics: Scalar quantities are those that are f