Dr. Phil's Home

Lectures in PHYS-2050 (H18)

Updated: 29 April 2008 Tuesday.

Week of April 28-May 2, 2008.

Monday 4/28: See Office Hours.

Tuesday 4/29: Grades due at Noon.

Next Dr. Phil Office Hours, Start of Summer-I Session on Monday 5 May 2008.

Week of January 7-11, 2008.

Monday 1/7: Class begins. The nature of studying Physics. Science education in the United States. Natural Philosophy. The Circle of Physics. Aristotle and the Greek Philosophers. Observation vs. Experiment - Dropping the book and the piece of paper (2 views).

Tuesday 1/8: Observation vs. Experiment - Zeno's Paradoxes. "Speed Limit 70" First Equation: Speed = Distance / Time. Development of Speed equation for Constant or Average Speed.

Wednesday 1/9: More about speed = distance / time. An Equation is a contract -- the left and right sides must be the same thing and all terms must have the same units. A simplified trip to the store -- The S-Shaped Curve. Distribute syllabus.

Thursday 1/10: Acceleration. Physics Misconceptions: Things you think you know, are sure you know, or just assume to be true in the back of your mind... but aren't true. Aristotle was sure that heavier objects always fell faster than lighter objects, but we did a demostration on Monday which showed that wasn't always true. Example: You're driving a car. To speed up, you need to put your foot on the accelerator (gas pedal), so YES, you are accelerating -- True. To drive at a constant speed, you must still have your foot on the accelerator, so YES, you are accelerating -- Not True because constant v means a = 0. To slow down, you must take your foot off the accelerator and put it on the brake pedal, so NO, you are not accelerating -- Not True because v is changing, so a < 0 (negative). Integrating to find the set of Kinematic Equations for constant acceleration. Kinematic Equations for Constant Acceleration. The Equation Without Time -- Avoiding the Quadradic Formula. Q1 and your PID number. (If you missed class on this day, check with Dr. Phil sometime soon.)

Friday 1/11: The fundamental equations of motion are based on the calculus: x, v and a are related by derivatives (slopes) and integrals (areas under the curve). v = dx/dt, a = dv/dt = d²x/dt². There are higher derivatives. For example, jerk is j = da/dt = d²v/dt² = d³x/dt³. SI Metric System. What do we mean by Measurements? "Units will save your life." Topic 1 assigned. (Click here for a copy of the handout.)

Week of January 14-18, 2008.

Monday 1/14: Class canceled by Dr. Phil due to illness. Sorry for the inconvenience.

Remember: PHYS-2060 Lab Begins This Week

Tuesday 1/15: What is "1 m/s"? We need a few benchmark values to compare English and SI Metric quantities. 60 m.p.h. = 26.8 m/s. 1.00 m/s = slow walking speed. 10.0 m/s = World Class sprint speed. (5/13/06 Sa: new World Record in 100m dash -- 9.76 seconds) What do we mean by a = 1 meter/sec² ? You cannot accelerate at 1 m/s² for very long. Types of Motion: No Motion (v=0, a=0), Uniform Motion (v=constant, a=0), Constant Acceleration (a=constant). We generally cannot accelerate for very long. Free fall, ignoring air resistance -- all objects near the surface of the Earth will fall at an acceleration g = 9.81 m/s². Example: acceleration and time for a bullet fired from a rifle.

Wednesday 1/16: Dr. Phil's Reasonable Significant Figures. (Click here for a copy of the handout.) There are six kinematic variables for constant acceleration in 1-D: x0, x, v0, v, a and t. Example: car accelerating from rest. Q2 in-class.

Thursday 1/17: Speed. 60 m.p.h. = "A Mile A Minute". (1848: The Antelope) The P-O-R (Press-On-Regardless) road rally problem. "You can't average averages." Motion in Two-Dimensions: x and y directions are perpendicular to each other. You may be able to break it down into two one-dimensional problems, connected by time, which you can already solve. The kinematic equations for constant acceleration in xand y, and y preloaded for freefall: ay = -g. Q3 Take-Home, due Tuesday 22 January 2008 in class or by 5pm. Note: parts (a)-(c) are for constant acceleration, (d)-(e) for constant jerk.

Friday 1/18: The consequences of Falling Down... ...and Falling Up. The Turning Point ( v=0 but a = -g during whole flight). The illusion of "hanging up there in the air" at the turning point. Types of Motion: No Motion (v=0, a=0), Uniform Motion (v=constant, a=0), Constant Acceleration (a=constant). Motion in Two-Dimensions: You may be able to break it down into two one-dimensional problems, connected by time, which you can already solve. (The guy with the fedora and the cigar.)

Week of January 21-25, 2008.

Monday 1/21: MLK Day to Honor Dr. Martin Luther King, Jr. -- Classes Do Not Meet at WMU -- University-wide activities.

Tuesday 1/22: Dr. Phil apologizes for being late to class due to slow roads. Solution to The guy with the fedora and the cigar problem. There are 6 variables from the first dimension (x0, x, v0x, vx, ax, t), but only 5 from the second (y0, y, v0y, vy, ay), because time is the same. Another problem with two motions linked by time: Classic Simple Pursuit (Cop and the Speeder). Same Place at the Same Time. Our algebra for car 1 and car 2, we cancelled a factor of t at one point -- this represents t = 0, which by definition is also a solution. But... because our problem is Simple Pursuit, when the car 2 reaches car 1, the cop is traveling at twice the speed of the speeder.

Wednesday 1/23: Two kinds of numbers: Scalars (magnitude and units) and Vectors (magnitude, units and direction). Adding and subtracting vectors: Graphical method. To generate an analytical method, we first need to look at some Trigonometry. Right Triangles: Sum of the interior angles of any triangle is 180°, Pythagorean Theorem (a² + b² = c²). Standard Angle (start at positive x-axis and go counterclockwise). Standard Form: 5.00m @ 30°. Practical Trigonometry. SOHCAHTOA. First Sample Exam 1 (Click here for a copy.) Q4 Take-Home, now due Monday 28 January 2008 in class or by 5pm.

Thursday 1/24: Adding and subtracting vectors: Analytical method. (Check to make sure your calculator is set for Degrees mode. Try cos 45° = sin 45° = 0.7071) Why arctangent is a stupid function on your calculator. Finding the final vector velocity of The guy with the fedora and the cigar problem. Recall our Simple Pursuit problem the other day: Our algebra for car 1 and car 2, we cancelled a factor of t at one point -- this represents t = 0, which by definition is also a solution. Q5 Take-Home, due Tuesday 29 January 2008 in class or by 5pm.

Friday 1/25: Regarding Q4 parts (d) and (e), now due Monday: How many unknown variables are there? Dr. Phil comes up with seven (x1, t1, x2, v2, t2, x3, t3), and then finds seven equations. In theory, 7 equations in 7 unknowns can be solved using the rules of algebra. However, if you can't make that work, you might want to try setting the total time to 30.0 sec or 35.0 sec, and trying to force a solution. Ballistic (or Projectile) Motion -- applies equally to a thrown football and a cannonball. Still working with ax = 0 and ay = -g. History of early cannons. Second Sample Exam 1 (Click here, here and here for a copy.)

Week of January 28-February 1, 2008.

Monday 1/28: Projectile or Ballistic Motion. Two Dangerous Equations. You can only use the Range Equation if the Launch Height = Landing Height. But the sin (2*theta) term in the Range Equation means that (1) 45° gives the maximum range for a given initial velocity and (2) that all other angles have a complementary angle (90° - theta) that gives the same range (but a different time and height). High and low trajectories for Range Equation. Third Sample Exam 1 (Click here and here for a copy.)

Tuesday 1/29: DVD movie clips: (1) Top Gun (Accelerations -- launching and recovering jets from an aircraft carrier. During launch, the plane drops off the deck because it isn't quite up to flying speed yet. Which brings us to the next movie...). (2) Speed (You have to have some positive v0y if you want to jump a gap -- even with a speeding bus.) Q6 in-class.

Wednesday 1/30: Class cancelled. Dr. Phil declares a Personal Sn*w Day, due to the high winds and treacherous icy roads between here and there. Nearly every school except WMU is closed. Exam 1 moved to Friday 1 February 2008, so you can still have one day to ask questions.

Thursday 1/31: Exam 1. Uniform Circular Motion (UCM): speed is constant, but vector velocity is not; magnitude of the acceleration is constant, but the vector acceleration is not. Velocity is tangent to circle, Centripetal Acceleration is perpendicular to velocity and points radial INWARD. For UCM, ac = v²/r. Space Shuttle in Low-Earth Orbit. (There's still gravity up there!).

Friday 2/1: Exam 1. WMU closed due to weather. No classes.

Week of February 4-8, 2008

Monday 2/4: Exam 1. (Rescheduled due to Sn*w Day.)

Tuesday 2/5: Uniform Circular Motion (UCM) continued: Example of a 2" hard disk drive spinning at 3600 rpm. Frequency (Hz) f = 1 / T. With spinning objects is very easy to come up with enormous centripetal accelerations. Spinning objects and "the plane of death" when pieces break off - the pieces become ballistic with an initial velocity vector pointing in the last tangential direction. Recap: Our studies so far have described "How" things move, and allow to say "When" and "Where" things move, but not "Why" things move. For that we have to start talking about Forces -- and that means Newton. Some stories about Sir Isaac Newton.

Wednesday 2/6: Some stories about Sir Isaac Newton. Zeroeth Law - There is such a thing as mass. Mass is a measure of how much "stuff" an object made of matter contains. SI unit of mass = kilogram (kg). First Law - An object in motion tends to stay in motion, or an object at rest tends to stay at rest, unless acted upon by a net external force. The Normal Force is a contact force perpendicular to a contact surface. Second Law - F=ma. Third Law - For every action, there is an equal and opposite reaction, acting on the other body. (Forces come in pairs, not apples.) "If I were to punch the wall, then the wall punches back." The Normal Force and the weight may be equal-and-opposite forces, but if they both apply to the same object, this is First Law, not Third Law. Q7 Take-Home, due Friday 8 February 2008.

Thursday 2/7: Force is a vector. Free Body Diagrams. Normal Force (Normal = Perpendicular to plane of contact). Sum of forces in x or y equations. SI unit of mass = kilogram (kg). SI unit of force = Newton (N). English unit of force = pound (lb.). English unit of mass = slug (Divide pounds by 32.). Pushing a 125 kg crate around. (Near the surface of the Earth, you can use the relationship that 1 kg of mass corresponds [not "equals"] to 2.2 lbs. of weight. So multiple 125 by 2 and add 10%... 250 + 25 = 275... so a 125 kg crate has a weight of mg = 1226 N or 275 lbs.). Variations as we allow for an applied force that it at an angle. "The Normal Force is NOT automatically present -- you have to be in contact with a surface. The Normal Force does NOT automatically point up -- FN is perpendicular to the surface. The Normal Force is NOT automatically equal to the weight. FN = mg only if there are no other forces in the y-direction."

Friday 2/8: Continue with the 125 kg crate. Variations as we allow for an applied force that it at an angle. Push down and Normal Force increases; pull up and Normal Force decreases -- though it cannot go negative. "You can't push on a rope." Since the force from a wire/string/rope/chain/thread/etc. can only be in one direction, Dr. Phil prefers to call such forces T for Tensions rather than F for Forces. Simple pulleys (Massless, frictionless, dimensionless, only redirect the forces). "There is no free lunch." The bracket for the pulley will have to support a force greater than the weight of the hanging object. Mechanical advantage: multiple pulleys allow us to distribute the net force across multiple cables or the same cable loop around multiple times. Tension in the cable is reduced, but you have to pull more cable to move the crate. Q8 Take-Home, due Tuesday 12 February 2008.

Week of February 11-15, 2008.

Monday 2/11: Atwood's Machine: Two blocks whose motion is link via a common cable and a pulley. Note that though they have a common magnitude of both speed and acceleration, the velocity vector has no bearing on either the F.B.D. or the solution to the Tension and acceleration. Hanging a sign with angled wires -- still the same procedure: Sketch of the problem, Free Body Diagram, Sum of Forces equations in the x- and y-directions, solve for unknowns. Need to deal with Friction -- two kinds (static and kinetic) -- but will next deal with inclined planes. First Sample Exam 2. (Click here for a copy.)

Tuesday 2/12: Change the co-ordinate system, change the rules. In the tilted x'-y' coordinates, this is a one-dimensional problem, not two-dimensional. Two kinds of Friction: Static (stationary) and Kinetic (sliding). For any given contact surface, there are two coefficients of friction, µ, one for static and one for kinetic. Static is always greater than kinetic. Static Friction is "magic", varying between zero and its maximum value of µ times the Normal Force. Kinetic Friction is always µ times the Normal Force. Demonstration of block sliding down inclined plane with friction. Finding the coefficient of static friction by tilting. µs = tan(thetamax). Similar for kinetic friction, except one has to tap the board to "break the static friction barrier". Rubber on concrete. Tires rolling with friction on good roads -- this is static friction not kinetic friction because the tires aren't sliding on the pavement. Q9 Take-Home quiz, due Thurday 14 February 2008.

Wednesday 2/13: Static & Kinetic Friction continued: Friction while driving. Rubber on dry concrete, coefficients are 1.00 and 0.800 . Tires rolling with friction on good roads -- this is static friction not kinetic friction because the tires aren't sliding on the pavement. Anti-Lock Brakes and Traction Control. Examples using our 125 kg crate sliding on the floor. If object is at rest, need to "test" to see if an applied external force exceeds the maximum static friction force ("breaks the static friction barrier"). Static Friction can vary from zero to its max value in either direction.

Thursday 2/14: Valentine's Day (not a WMU holiday). We need another Physics quantity, one which describes the "relentless quality" of motion, one that includes mass. Inertial or Linear momentum: p = m v. This is a vector. Newton's Form of the Second Law (differential form). Impulse (integral form). NOTE: The difference between Work and Impulse, is that one integrates the Force over distance, the other Force over time. More Conservation Laws in Physics. Two extremes in collisions: Totally Elastic Collision (perfect rebound, no damage) and Totally Inelastic Collision (stick together, take damage). Linear momentum is conserved in all types of collisions. Example: The Yugo and the Cement Truck. Head-on Collisions. Q10 Take-Home quiz, due Tuesday 19 February 2008.

Friday 2/15: Totally Inelastic Collisions (con't.) Three example collisions: head-on, rear-end, 2-D. (The Non-Collision -- if the car following is going slower, it isn't going to run into the car ahead. PTPBIP.) What happens in a wreck. How airbags work.

Week of February 18-22, 2008.

Monday 2/18: What's the opposite of a collision? An explosion. Or recoil. Example: A pitcher on ice skates at rest -- when he hurls a fastball to the right, he goes to the left. Total momentum of the system remains constant (in this case, zero). The Rocket Equation -- use conservation of momentum. Second Sample Exam 2 (Click here and here for a copy.)

Tuesday 2/19: Dr. Phil has canceled class today due to road conditions. Read about my Tuesday here.

Wednesday 2/20: Work: A Physics Definition (Work = Force times distance in the same direction). Work = Energy. Pay particular attention to Units. Dot products: one of two methods of multiplying two vectors -- this method generates a scalar, which is a good thing because Work happens to be a scalar, which is Work's virtue (i.e. why we care). Dot products: run through two 3-dimensional vector case. Q11 is a Take-Home quiz, made available on Wednesday 20 February 2008, and due Tuesday 26 February 2008.

Thursday 2/21: Kinetic Energy -- an energy of motion, always positive, scalar, no direction information. Work-Energy Theorem (net Work = Change in K.E.). Lose angle and directional information because energy is a scalar, not a vector. Potential Energy: Storing energy from applied work for later. Gravitational P.E. = mgh. Conservation Laws are very important in Physics. Conservation of Total Mechanical Energy (T.M.E. = K.E. + P.E.).

Friday 2/22: Return X1. Conservation of Total Mechanical Energy (T.M.E. = K.E. + P.E.). Lose angle and directional information because energy is a scalar, not a vector. Example: Roller-Coaster. If speed at top of the first hill is about zero, then this P.E. is all we have. Cannot get higher, but we can change height for speed. Q12 Take-Home quiz, due Tuesday 26 February 2008.

Sigh -- there appears to be an error in some of the grading of Problem 2 on Exam 1, which also may affect the star points. We will address this on Monday.

Week of February 25-29, 2008.

Monday 2/25: Conservation of Total Mechanical Energy (T.M.E. = K.E. + P.E.). Demo: a suspended bowling ball shows conservation of T.M.E. All P.E. when swings up to a stop on either side, all K.E. at bottom of swing. (There must be non-conservative forces, such as air resistance and friction in the pivot point on the ceiling -- because the bowling ball never quite gets up as high as it starts.) Totally Elastic Collisions -- both K.E. and linear momentum conserved. Close approximations: The Executive Time Waster. NOTE: Will collect X1 papers Tuesday or Wednesday with points taken off for not having parentheses in integral in parts 2(a), etc.

Tuesday 2/26: Why you want inelastics collisions in a wreck. "Adobe: The Little Car Made of Clay". The Ballistic Pendulum -- We can find the speed of a projectile through an Inelastic Collision followed by Conservation of TME. Hooke's Law (Spring force) is a second conservative force, which we can also write as a P.E. Q13 Take-Home, due Thursday 28 February 2008. NOTE: Give the answer to part (b) in Standard Form.

Wednesday 2/27: Resistive Forces: Air Resistance. Low speed and high speed air resistance. If allowed to drop from rest, then a real object may not free fall continuously, but may reach a Terminal Velocity (Force of gravity down canceled by Drag force up) and doesn't accelerate any more. Ping-pong balls versus turkeys or pennies. World's Record Free-Fall. Third Sample Exam 2 (Click here for a copy.)Turn in your X1 if you need a Problem 2 regrade.

Thursday 2/28: Exam 2.

Friday 2/29: Spirit Day. <No Classes> Effective start to Spring Break.

Week of March 10-14, 2008.

Monday 3/10: Classes resume. Power = Work / time. Since W=Fd, then P=W/t = Fd/t = Fv for constant Force and constant speed. Translating Linear physics to Rotational physics (as "easy" as changing Roman/English variables to Greek). The radian is a "quasi-unit" -- it's not really a unit, but represents a fraction of a circle. (We can "wish" it away when we need to.) Angular position, angular velocity.

Tuesday 3/11: Translating Linear physics to Rotational physics: Angular position, angular velocity, angular acceleration, angular force = torque. Newton's 3 Laws of Motion applied to rotations. Angular momentum.

Wednesday 3/12: Rotational Work, rotational K.E., angular momentum. Extended Objects: We have been treating our objects really as dimensional dots, that have been allowed to have mass. Now we want to start considering how that mass is distributed. An airplane with mass unevenly concentrated in front, back or to one side, may not be flyable. Center of mass is a "weighted average", meaning it combines a position with how much mass is involved. Center of mass in the x-direction: discrete case and 1-D uniformly distributed mass (Example: A meter stick balances at the 50 cm mark.) We have been calculating the motion of the center of mass all this time. Q14 Take-Home quiz, due Thursday 13 March 2008.

Thursday 3/13: Center of Mass (con't.): 2-D uniformly distributed mass -- Center of mass in x-direction and in y-direction. Rectangular plate. Note that the center of mass value depends on the coordinate system, but the center of mass point remains in the same place. Triangular plate -- parameterizing y = y(x) (y as a function of x). Mass per unit length (lamda), mass per unit area (sigma). Demo: Suspending real objects from different points to find the center of mass -- hung from the center of mass, the object is perfectly balanced. Include: irregular plate, rectangular plate, triangular plate, Michigan (Lower Pennisula), Florida. The center of mass does NOT have to be located ON the object -- the obvious example is a ring or hoop, where the center is empty. Demo: The toy that "rolls uphill" -- actually, whether with the cylinder or the double-cone, the center of mass is going downhill. Start discussion of Moment of Inertia. We will be reproducing the results from Table 10-2 in your textbook, but you can use these results on your Formula Card and on this next quiz. Q15 Take-Home, due Thursday 20 March 2008. NOTE: That the quiz has two pages. If done correctly, (b) = (e) and (c) = (d).

Friday 3/14: Moment of Inertia, discrete case. Parallel Axis Theorem. Moment of Inertia by Integration, Double- and Triple-Integrals in Rectangular, Polar, Cylindrical and Spherical Co-ords. An aside on Polar Coordinates and the integration of dL to get C = 2 pi R and dA to get A = pi R². Moment of Inertia of Ring, I = MR² by inspection, by integration.

Week of March 17-21, 2008

Monday 3/17: Return X2. Moment of Inertia of Ring, Solid Disk. Start of Spherical Coordinates.

Tuesday 3/18: Moment of Inertia by Integration, Double- and Triple-Integrals in Spherical Co-ords. Moment of Inertia of Ring, Solid Disk. Moment of Inertia of Solid Cylinder, Hollow Sphere, Solid Sphere. Rotational K.E., Rolling objects down an incline. Q16 Take-Home, due Thursday 20 March 2008.

Wednesday 3/19: The Cross Product and Right-Hand Rule (R.H.R.). Using Right Hand Rule to assign directions to x,y,z coordinates and the sense of rotations for theta, omega (angular velocity), alpha (angular acceleration) and tau (torque) -- the vectors for these variables ends up pointing up or down the axis of rotation. Torque = r F, when applying a linear force perpendicular to a radius line to the axis of rotation. (Most torques we apply are done this way.) A "breaker bar" is a pipe used to extend the handle of a wrench -- this increases the torque for a given applied force, but the use of a breaker bar may damage the thing you are trying to torque. Angular momentum L = r p, when the linear momentum vector is perpendicular to the radius vector. The Cross Product (or Vector Product) is the exact opposite of the Dot Product (or Scalar Product). Multiplying two vectors together by a cross product gives us another vector (instead of a scalar). And the cross product is not commutative, vector-A × vector-B = - (vector-B × vector-A), so the order is paramount.

Thursday 3/20: How we solve force problems: (1) Free Body Diagram, (2) Sum of Forces equations, (3) Newton's Laws. How we solve torque problems: (1) Free Rotation Diagram, (2) Sum of Torques equations, (3) Newton's Laws. Real pulleys vs. Perfect Massless Pulleys. The acceleration of the Atwood's Machine with a real pulley is less than the acceleration with a simple pulley, because it takes work and energy to rotate the real pulley. The "Free Rotation Diagram". Statics: objects not translating in any direction and objects not rotating in any direction. Free Body Diagrams, Free Rotation Diagrams (sum of forces, sum of torques). Teeter-Totter. First Sample Exam 3. (Click here for a copy.) Simple bridges.Q17 is a Take-Home, due Tuesday 25 March 2008.

Friday 3/21: Statics problems (no translation, no rotation about any axis) con't. Loaded bridge. Diving board. The ladder leaning on the wall. Choose pivot point at floor to eliminate two of the three unknown forces from the sum of torques equation. Homework: Figure out whether the perpendicular components of the weight and the wall (normal) force use sin or cos of theta, the angle the ladder makes with the floor. Is there enough static friction to hold it? (theta = 70°, m = 15.0 kg, L = 3.00 m, mu's of 0.600 and 0.700 for floor only, no friction with wall.) If you're keeping score at home, Statics is in Chapter 12 of your book, and teeter-totters and the leaning ladder are both examples in the book.

Week of March 24-28, 2008.

Monday 3/24: Extended Objects -- Allowing for Deformation. Young's Modulus. Tension, Compression.

Tuesday 3/25: Young's Modulus. Tension, Compression. Pre-Stressed Concrete. Simulating years of service of a device by cycling under load.

Wednesday 3/26: Bulk Modulus. Newton's Universal Law of Gravity (or Newton's Law of Universal Gravity). Gravity is attractive between any two masses. Same magnitude, opposite direction by Newton's Third Law. Use Universal Gravity to check "g". The value we calculate is close, 9.83m/s², which turns out to be only off by 0.2%. Why is it off? Because using Univeral Gravity in this manner makes the assumption that the entire Earth is uniform and homogenous from the surface to the core -- which it is not. We would need to integrate over layers to get the observed value of 9.81m/s². The problem of determining G and the mass of the Earth. The four fundamental forces in nature, from weakest to strongest: Gravity, Electromagnetism, Weak Nuclear Force, Strong Nuclear Force. Gravity may be the weakest, but it holds us onto this planet and "binds the galaxies together". Story of researchers thinking they'd discovered a "fifth" force -- turned out to be Moon's attraction.

Thursday 3/27: g(r). The Shuttle in Low Earth Orbit (Revisited). Second Sample Exam 3. (Click here, here and here for a copy.) Q18 In-Class. Q19 Take-Home, due on Tuesday 1 April 2008 (no fooling!)

Friday 3/28: Tides (high/low, spring/neap). Planetary Orbits. Ptolemy to Copernicus to Johannes Kepler. Epicycles, elliptical orbits and Occam's Razor. Tycho Brahe's observatory and his data.

Week of March 31-April 4, 2008.

Monday 3/31: Epicycles, elliptical orbits and Occam's Razor. Kepler's First Law -- All orbits are ellipses, with the larger mass at one focus. Circular orbits are a special case where the semi-major axis is the same as the semi-minor axis: a = b = R. Kepler's Second Law -- The Equal Area Law is equivalent to a statement of Conservation of Angular Momentum. Kepler's Third Law -- T² = C R³, where R is the radius of a circular orbit, or the average distance in an elliptical orbit. There is one value for the constant C for every orbital system, i.e. one C for objects orbiting the Earth, another C for objects orbiting the Sun. Example: Using our data from the Space Shuttle's Low Earth Orbit, we can calculate C for Earth. Then plug in the R for the Moon's orbit and get an orbital period of 27.4 days, which is essentially correct. NOTE: There are several definitions of the lunar month -- the one normally used is the time to return to the same place in the sky, which because the Earth is going around the Sun, is slightly MORE than one orbit and is about 28 days.

Tuesday 4/1: April Fool's Day (not a WMU holiday). Kepler's Third Law -- T² = C R³, where R is the radius of a circular orbit, or the average distance in an elliptical orbit. There is one value for the constant C for every orbital system, i.e. one C for objects orbiting the Earth, another C for objects orbiting the Sun. Example: Using our data from the Space Shuttle's Low Earth Orbit, we can calculate C for Earth. Then plug in the R for the Moon's orbit and get an orbital period of 27.4 days, which is essentially correct. NOTE: There are several definitions of the lunar month -- the one normally used is the time to return to the same place in the sky, which because the Earth is going around the Sun, is slightly MORE than one orbit and is about 28 days. Stability of objects -- demo with heavy lead brick. (Additional demo of inertia -- volunteer doesn't feel hammer blow when hand is under lead brick.) Falls over when center-of-mass is unsupported. Tall & skinny objects much easier to tip over, than low & wide.

Wednesday 4/2: Review for X3. Stability of objects -- not tipping over. Rollovers, "J-Turns" (a U-turn with a rollover), Jeep CJ vs. Jeep YJ. Ground clearance and the HUMVEE. Riding lawn mowers and hills.

Thursday 4/3: Exam 3.

Friday 4/4: Three Classical States of Matter: Solid, Liquid, Gas. Combinations: Condensed Matter (covers both Solids and Liquids) and Fluids (covers both Liquids and Gasses). Two Extreme States of Matter: Plasma (electrons stripped off, high temperature), Cryogenics (extreme cold, odd behavior). Mass-to-Volume Ratio (Density). NOTE: Do not confuse the Density of the Materials with the Mass-to-Volume Ratio of the OBJECT. Density of Water built into the SI metric system (1 gram/cm³ = 1000 kg/m³). Floating on the Surface: Mass-to-Volume Ratio of the boat < Mass-to-Volume Ratio of the Liquid.

Week of April 7-11, 2008.

Monday 4/7: Last Day to turn in a Draft Paper if you wish (or if you picked a combo NOT in the list and you have to turn in a Draft). Mass-to-Volume Ratio (Density). NOTE: Do not confuse the Density of the Materials with the Mass-to-Volume Ratio of the OBJECT. Density of Water built into the SI metric system (1 gram/cm³ = 1000 kg/m³). Floating on the Surface: Mass-to-Volume Ratio of the boat < Mass-to-Volume Ratio of the Liquid. Why Boats Float. Example: Front lab table as a 250 kg boat with 4.00 m³ volume. Buoyant Force = Weight of the Boat = Weight of the Water Displaced by the Submerged Part of the Boat.

Tuesday 4/8: Three Classical States of Matter: Solid, Liquid, Gas. Combinations: Condensed Matter (covers both Solids and Liquids) and Fluids (covers both Liquids and Gasses). Pressure = Force / Area. SI unit: Pascal (Pa). Example: Squeezing a thumbtack between thumb and forefinger. One Atmosphere standard air pressure = 1 atm. = 14.7 psi = 101,300 Pa. Pressure at a depth due to supporting the column of liquid above. The difference between Gauge Pressure (pressure difference inside and out, can be positive, negative or zero) and Absolute Pressure (total pressure, always positive or zero only for vacuum). Water pressure = 101,300 Pa at depth h = 10.33 m. Why you need a qualified SCUBA instructor. Q20 Take-Home, due Thursday 10 April 2008.

Wednesday 4/9: Pressure at a depth due to supporting the column of liquid above. Water pressure = 101,300 Pa at depth h = 10.33 m. Why you need a qualified SCUBA instructor. Using a column of liquid to make a barometer to measure air pressure. Switch from water to mercury changes h at 1 atm. from 10.33 m to 0.759m. The aneroid barometer. Pressure from a column of liquid looks like P.E. Create a Kinetic Pressure term which looks like K.E. to create Bernoulli's Equation and the Continuity Equation. Water Tower and the Faucet Problem. Why the water tower needs a vent.

Thursday 4/10: Bernoulli's Equation and the Continuity Equation. When speed goes up, pressure goes down. Example: The aspirator -- a vacuum pump with no moving parts. Example: Air flow around a wing. (Faster air over top means lower pressure on top, so net force is up -- generating Lift.) The spoiler is a vent door in a wing designed to allow air to flow from bottom to top and thus "spoiling" the pressure difference and "spoiling" the lift. First Sample Final Exam. (Click here and here for a copy.) First Day to turn in your Topic 1 Paper.

Friday 4/11: Last thoughts on Bernoulli, Lift and spoilers. "Canyons" in skyscraper cities -- windows popping out of the Hancock Tower in Boston. Rotating baseballs. The Mackinac Bridge -- inside lanes are open metal grates and cannot support a pressure difference. Periodic, Repeating and Oscillating Motions. Characterized by a Period T (the repeat time) and a Frequency f (how many repeats in a given time). Revisit Mass on a spring. F = -kx = ma. Generates a 2nd Order Differential Equation - sine & cosine solutions. Second Sample Final Exam. (Click here for a copy.) Q21 Take-Home, due Tuesday 15 April 2008.

Week of April 14-18, 2008.

Monday 4/14: The Moons of Mercury: Looking Up and Looking Down -- special presentation of Saturday's talk at the Michigan Section of the American Association of Physics Teachers (MIAAPT) meeting here at WMU. Revisit Mass on a spring. F = -kx = ma. Generates a 2nd Order Differential Equation - sine & cosine solutions. Any time you have a conservative linear restoring force that can act as periodic motion you have a Simple Harmonic Oscillator that undergoes Simple Harmonic Motion. S.H.O. & S.H.M. Uniform Circular Motion (U.C.M.) as two S.H.O.'s (x- and y-components). End of Grace Period for Topic 1 papers (5pm).

Tuesday 4/15: Simple Pendulum. Physical Pendulum. Mass on a spring has an angular frequency omega = 2pi f= sqrt(k/m). Simple Pendulum -- omega = sqrt(g/L). For a Grandfather clock with a simple pendulum, period T = 2.00 sec gives L = 0.9940 m. For a mantlepiece clock with a simple pendulum, period T = 1.00 sec, L = 0.2485 m. Grandfather clocks won't work right in space or on the Moon. (But a tortional pendulum mantlepiece clock will.) Physical Pendulum -- omega = sqrt (mgd / I). At first it looks like the mass factors into the angular frequency. But it is not the mass, but how it is distributed, because the moment of inertia I also contains the mass m. End of Grace Period for Topic 1 papers with a Draft (5pm).

Wednesday 4/16: X3 returned. Quick mentions: Torsional pendulum. Damping with Restorative Force = - bv. Underdamped, overdamped, critically damped. Driven or force oscillator. Resonance at critical frequency. Car suspensions and washboard roads. Q22 Take-Home quiz, due Friday 18 April 2008.

Thursday 4/17: The Laws of Thermodynamics. (Zeroeth Law -- There is such a thing as temperature.) Entropy examples -- It takes work to clean or restore things. Left to themselves, everything falls apart. The Heat Engine and Three Efficiencies (Actual, Carnot and 2nd Law). Fuel Economy (miles per gallon) is not an Efficiency. There is no conspiracy to keep big 100 m.p.g. cars out of our hands. To use less fuel, do less work. Handout of "Lost Lectures". (Here's a partial version of what was handed out.)

Friday 4/18: Last Day of Class. And they even tried to stop up with Earthquakes! To use less fuel, do less work. Smaller, lighter cars with smaller, lighter engines. To improve efficiency, can reduce TC or raise TH . Reverse the arrows in the Heat Engine and you get a Refrigerator. Cannot place an open refrigerator or a window air conditioner in the middle of a room and cool the room, because the exhaust heat to the hot side includes the heat pulled from the cold side plus the work done on the compressor. A Heat Pump is a reversible system which cools inside of the house in summer and heats the inside of the house in winter -- just because it is cold outside, doesn't mean there is not heat energy Q in the outside air. (There has to be, otherwise the air would be at 0 K.)

FINALS Schedule

All Monday 11 am classes Thursday April 24 10:15 am - 12:15 pm This is our actual Scheduled Final Exam time, but about half the class has a final just before at Parkview.

All Tuesday 11 am classes Wednesday April 23 10:15 am - 12:15 pm In Theory, this time slot could be ours as well, since we have 1110 Rood at 11am everyday and no one should have a Tuesday 11am class separate from PHYS-2050 Honors. ADOPTED.