## Lectures in PHYS-205 (13)

Updated: 11 June 2003 Wednesday. (18 September 2003)

### Week of June 9-13, 2003.

Monday 6/9: 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, angular acceleration, angular force = torque. Newton's 3 Laws of Motion applied to rotations. Rotational Work, rotational K.E., angular momentum. Why we need a "rotational mass": Moment of Inertia. The Cross Product and Right-Hand Rule (R.H.R.). Moment of Inertia of a long thin rod: (1) axis about center of mass, (2) axis about end. Q13 Take-Home now due Tuesday 10 June 2003.

Tuesday 6/10: Moment of Inertia by Integration, Double- and Triple-Integrals in Rectangular, Polar, Cylindrical and Spherical Co-ords. Moment of Inertia of Ring, Solid Disk, Solid Cylinder, Hollow Sphere, Solid Sphere. Rotational K.E., Rolling objects down an incline. The Race. Real pulleys vs. Perfect Massless Pulleys. The "Free Rotation Diagram". Q15 Take-Home, due Thursday 12 June 2003.

Wednesday 6/11: No Class. SPECIAL OFFICE HOURS: Noon to 3pm.

Thursday 6/12: Exam 3 moved to Friday the Thirteenth! First day to hand in Topic 1 papers.

Friday 6/13: Exam 3 re-scheduled.

### Week of May 5-9, 2003.

Monday 5/5: Class begins. Distribute syllabus. The nature of studying Physics. Science education in the United States. "Speed Limit 70"

Tuesday 5/6: Natural Philosophy. The Circle of Physics. Aristotle and the Greek Philosophers. Observation vs. Experiment - Dropping the book and the piece of paper (2 views). Zeno's Paradoxes. First Equation: Speed = Distance / Time. Development of Speed equation for Constant or Average Speed.

Wednesday 5/7: No Class

Thursday 5/8: A simplified trip to the store. Acceleration. Physics misconceptions. Integrating to find the set of Kinematic Equations for constant acceleration. Kinematic Equations for Constant Acceleration. The Equation Without Time -- Avoiding the Quadradic Formula. What is "1 m/s²"? You cannot accelerate at 1 m/s² for very long. So far we are doing motion in just one dimension. But that one direction can be vertical instead of horizontal. All objects near the surface of the Earth, in the absence of air resistance, fall and accelerate at the same rate, g = 9.81 m/s². That's nearly ten times the rate from before! (No wonder it hurts to fall out of a tree -- you get going really fast very quickly.) Jerk is a change in the acceleration.

Friday 5/9:

### Week of May 12-16, 2003.

Monday 5/12: 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. (The guy with the fedora and the cigar.) 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. 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. Q3 in-class.

Tuesday 5/13: Finding the final vector velocity of The guy with the fedora and the cigar problem. Q4 take-home, due Thursday 5/15.

Wednesday 5/14: No Class

Thursday 5/15: NOTE: Exam 1 moved to Monday 5/19, so you can have the weekend to study.

Friday 5/16:

### Week of May 19-23, 2003.

Monday 5/19: Exam 1.

Tuesday 5/20: Types of Motion studied so far: No motion, Uniform motion (v=constant, a=0), Constant Acceleration. 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. Space Shuttle in Low-Earth Orbit. (There's still gravity up there!). 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. 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. 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.)

Wednesday 5/21: No Class

Thursday 5/22: Some stories about Sir Isaac Newton. 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.). First sample example pages for Exam 2. Q7 in-class.

Friday 5/23: More pushing the 125 kg crate around: Variations as we allow for an applied force that it at an angle. "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. 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. 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. 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 Book sliding down inclined plane with friction. Second sample exam pages for Exam 2. Exam 1 returned. Q8 Take-Home, due Tuesday 5/27.

### Week of May 26-30, 2003.

Monday 5/26: MEMORIAL DAY HOLIDAY - No Class.

Tuesday 5/27: Elevator Problems. The Normal Force represents the "apparent weight" of the person in the elevator. For the elevator at rest or moving at constant speed, the Normal Force = weight, and the tension of the cable = weight of loaded elevator. But if there is an acceleration vector pointing up, the apparent weight and the tension of the cable increase; if the vector points down, the apparent weight and the cable tension decrease. In true Free Fall, without any air resistance, the Normal Force = 0 and you are floating. Example: NASA's VC-135 "Vomit Comet", which flies in parabolic arcs to gain about 30 seconds of free-fall at a time for experiments and training. Atwood's Machine: Two blocks whose motion is link via a common cable and a pulley. Q8 take-home due today. Q9 take-home, due Thursday 5/29. (Not available online.)

Wednesday 5/28: No Class.

Thursday 5/29: Revisiting UCM, now with the Centripetal Force, using F=ma. The Centrifuge and possible reasons why people talk of a "centifugal force" -- No such thing as Centrifugal Force. Why old-timers talk about "getting flung safely from a wreck". The story of the 50,000 rpm Ultra-Centrifuge and the Fresh Rat's Liver. The need for "Artificial Gravity" using UCM in long duration space missions. Examples: Minimum radius for safe turns at given speed v (level ground with friction, banked curved without friction). 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). Exam 2 scheduled. Moving to Monday 6/2, so you can have the extra weekend to study.

Friday 5/30: Dot products: run through two 3-dimensional vector case. Kinetic Energy -- an energy of motion, always positive, scalar, no direction information. Work-Energy Theorem (net Work = Change in K.E.). 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.). 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. Revisit example of the loop-the-loop from U.C.M. and determine height of Hill 1 in order to safely loop-the-loop. Power = Work / time. Demo: a suspended bowling ball shows conservation of T.M.E. Hooke's Law (Spring force) is a second conservative force, which we can also write as a P.E. Work done by non-conservative forces, like friction. DOUBLE QUIZ Q11-12 take-home, due TUESDAY 3 June 2003.

### Week of June 2-6, 2003.

Monday 6/2: Exam 2 re-scheduled.

Tuesday 6/3: Movie clip: 2001: A Space Odyssey (What would it look like to have use centripetal force for artificial gravity? Stanley Kubrick's 1968 movie showed us a large rotating space station and a smaller rotating carousel on a ship to Jupiter.) Video Clip: Skylab missions (motion in free fall). Linear momentum: p = m v. This is a vector. 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. Three example collisions: head-on, rear-end, 2-D.

Wednesday 6/4: No class.

Thursday 6/5: What happens in a wreck. How airbags work. Totally Elastic Collisions. Close approximations: The Executive Time Waster, the Physics of pool shots. More on car safety systems. Why you want inelastics collisions in a wreck. "Adobe: The Little Car Made of Clay". 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. Explosions = Backwards Collisions. Recoil. The Ballistic Pendulum (Inelastic Collision followed by Conservation of TME). 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. Demo: Tossing a stick across the room (1) javelin style and (2) with rotation -- in both cases the center of mass roughly follows the ballistic curve. Q13 take-home, due Monday 9 June 2003.

Friday 6/6: 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. The Rocket Equation -- use conservation of momentum. Discussion of why we use multi-stage rockets. Q14 in-class.