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Donald Albin

Lehigh University

Biography

I am currently a secondary education math teacher. However, I've taught all grade levels including elementary, middle school, high school, and community college. I pray that you find my content helpful.

Education

MS Mechanical Engineering
Lehigh University
MS Curriculum & Instruction
Shippensburg University of Pennsylvania
BS Engineering Science
Pennsylvania State University

Topics Covered

Sampling and Data
Probability Topics
Probability and Counting Rules
Parametric Equations
Polar Coordinates
Trigonometry
Introduction to Vectors
Complex Numbers
Matrices
Rational Functions
Systems of Equations and Inequalities
Introduction to Matrices
Functions
Linear Functions
Polynomials
Work
Kinetic Energy
Potential Energy
Energy Conservation
Moment, Impulse, and Collisions
Applying Newton's Laws
Rotation of Rigid Bodies
Dynamics of Rotational Motion
Equilibrium and Elasticity
Gravitation
Vectors
Thermal Properties of Matter
The First Law of Thermodynamics
The Second Law of Thermodynamics
Electromagnetic Waves
Wave Optics
Magnetic Field and Magnetic Forces
Mechanical Waves
Reflection and Refraction of Light
Temperature and Heat
Current, Resistance, and Electromotive Force
Direct-Current Circuits
Electromagnetic Induction
Alternating Current
Gravity, Planetary Orbits
Sampling and Simulation
Linear Regression and Correlation
Physics Basics
Motion Along a Straight Line
Motion in 2d or 3d
Sources of Magnetic field
Inductance
Differentiation
Derivatives
Applications of the Derivative
Applications of Integration
Newton's Laws of Motion
Introduction and Vectors
Motion
Atomic Physics
Electric Charge and Electric Field
Fluid Mechanics
Periodic Motion
Sound and Hearing
Applications of Newton’s Laws
Rotational Motion
Equations and Inequalities
Volume
Descriptive Statistics
Data Description

Donald's Textbook Answer Videos

08:25
Calculus: Early Transcendentals

Light enters the eye through the pupil and strikes the retina, where photoreceptor cells sense light and color. W. Stanley Stiles and B. H. Crawford studied the phenomenon in which measured brightness decreases as light enters farther from the center of the pupil. (see the figure.)

They detailed their findings of this phenomenon, known as the Stiles-Crawford effect of the first kind, in an important paper published in 1933. In particular, they observed that the amount of luminance sensed was not proportional to the area of the pupil as they expected. The percentage $ P $ of the total luminance entering a pupil of radius $ r mm $ that is sensed at the retina can be described by
$$ P = \frac{1 - 10^{-pr^2}}{pr^2 \ln 10} $$
where $ p $ is an experimentally determined constant, typically about $ 0.05 $.
(a) What is the percentage of luminance sensed by a pupil of radius $ 3 mm $? Use $ p = 0.05 $.
(b) Compute the percentage of luminance sensed by a pupil of radius $ 2 mm $. Does it make sense that it is larger than the answer to part $ (a) $?
(c) Compute $ \displaystyle \lim_{r\to 0^+} P $. Is the result what you would expect? Is this physically possible?

Source: Adapted from W. Stiles and B. Crawford, "The Luminous Efficiency of Ray Entering the Eye Pupil at Different Points." Proceedings of the Royal Society of London, Series B: Biological Sciences 112(1933): 428-50.

Chapter 4: Applications of Differentiation
Section 4: Indeterminate Forms and l'Hospital's Rule
Donald Albin
19:58
University Physics with Modern Physics

Firemen use a high-pressure hose to shoot a stream of water at a burning building. The water has a speed of 25.0 m/s as it leaves the end of the hose and then exhibits projectile motion. The firemen adjust the angle of elevation $\alpha$ of the hose until the water takes 3.00 s to reach a building 45.0 m away. Ignore air resistance; assume that the end of the hose is at ground level. (a) Find $\alpha$. (b) Find the speed and acceleration of the water at the highest point in its trajectory. (c) How high above the ground does the water strike the building, and how fast is it moving just before it hits the building?

Chapter 3: Motion in Two or Three Dimensions
Section 3: Projectile Motion
Donald Albin
08:13
University Physics with Modern Physics

At its Ames Research Center, NASA uses its large "20-G" centrifuge to test the effects of very large accelerations ("hypergravity") on test pilots and astronauts. In this device, an arm 8.84 m long rotates about one end in a horizontal plane, and an astronaut is strapped in at the other end. Suppose that he is aligned along the centrifuge's arm with his head at the outermost end. The maximum sustained acceleration to which humans are subjected in this device is typically 12.5$g$. (a) How fast must the astronaut's head be moving to experience this maximum acceleration? (b) What is the $difference$ between the acceleration of his head and feet if the astronaut is 2.00 m tall? (c) How fast in rpm (rev/min) is the arm turning to produce the maximum sustained acceleration?

Chapter 3: Motion in Two or Three Dimensions
Section 4: Motion in a Circle
Donald Albin
05:25
University Physics with Modern Physics

Two piers, $A$ and $B$, are located on a river; $B$ is 1500 m downstream from A ($\textbf{Fig. E3.32}$). Two friends must make round trips from pier $A$ to pier $B$ and return. One rows a boat at a constant speed of 4.00 km/h relative to the water; the other walks on the shore at a constant speed of 4.00 km/h. The velocity of the river is 2.80 km/h in the direction from $A$ to $B$. How much time does it take each person to make the round trip?

Chapter 3: Motion in Two or Three Dimensions
Section 5: Relative Velocity
Donald Albin
06:57
University Physics with Modern Physics

Two blocks connected by a light horizontal rope sit at rest on a horizontal, frictionless surface. Block $A$ has mass 15.0 kg, and block $B$ has mass $m$. A constant horizontal force $F$ = 60.0 N is applied to block $A$ ($\textbf{Fig. P4.40}$). In the first 5.00 s after the force is applied, block $A$ moves 18.0 m to the right. (a) While the blocks are moving, what is the tension $T$ in the rope that connects the two blocks? (b) What is the mass of block $B$?

Chapter 4: Newton's Laws of Motion
Donald Albin
09:17
University Physics with Modern Physics

In a truck-loading station at a post office, a small 0.200-kg package is released from rest at point A on a track that is onequarter of a circle with radius 1.60 m ($\textbf{Fig. P7.57}$). The size of the package is much less than 1.60 m, so the package can be treated as a particle. It slides down the track and reaches point $B$ with a speed of 4.80 m/s. From point $B$, it slides on a level surface a distance of 3.00 m to point $C$, where it comes to rest. (a) What is the coefficient of kinetic friction on the horizontal surface? (b) How much work is done on the package by friction as it slides down the circular arc from $A$ to $B$?

Chapter 7: Potential Energy and Energy Conservation
Donald Albin
1 2 3 4 5 ... 571

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