Welcome back to Physics 211 Today s agenda: Rotations What s on the exam? Relative motion Physics 211 Spring 2014 Lecture 04-1 1 ask a physicist Why are neutrinos faster than light (photons)? I thought light was the fastest thing around! lso are there any superluminal speeds? Physics 211 Spring 2014 Lecture 04-1 2 1
Demo: Loop-de-Loop (need volunteer!) Draw the components of the acceleration vector at the sides and top of the loop-de-loop Physics 211 Spring 2014 Lecture 04-1 3 Clicker 4-1.4: What is the acceleration vector for object speeding up from rest at point? Physics 211 Spring 2014 Lecture 04-1 4 2
cceleration vectors for object speeding up: Tangential and radial components (or parallel and perpendicular) Physics 211 Spring 2014 Lecture 04-1 5 Summary Components of acceleration vector: Parallel to direction of velocity: (Tangential acceleration) How much does speed of the object increase? Perpendicular to direction of velocity: (Radial acceleration) How quickly does the object turn? Physics 211 Spring 2014 Lecture 04-1 6 3
Relating linear and angular kinematics Linear speed: v = (2πr)/T = ω r Radial acceleration: a rad = v 2 /r = ω 2 r Tangential acceleration: a tan = r α = 0 + t = 0 + 0 t + 1 2 t2 2 = 2 0 +2 Physics 211 Spring 2014 Lecture 04-1 7 Sample problem small steel roulette ball rolls around inside of a 30-cm diameter roulette wheel. It is spun at 150 rpm, but it slows down to 60 rpm over an interval of 5.0s. ssume constant angular acceleration. How many revolutions does the ball make during these 5.0s? Physics 211 Spring 2014 Lecture 04-1 8 4
Midterm 1: in a week and a half! (2/11) In Stolkin (here!) at the usual lecture time Material covered: Textbook chapters 1-4 Lectures up through 2/4 (slides online) Wed/Fri recitation activities Homework assignments You will be given a formula sheet at the exam. copy of this sheet is available on the course website You should bring a calculator, but you must bring your own, and it can not be a phone. You may not store any equations in memory, and midterm proctors may request to see your calculator during the exam. Exam accommodations: must take exam at ODS I need the request form by THIS THURSDY Physics 211 Spring 2014 Lecture 04-1 9 What types of problems should I practice? Everything we covered in lecture/homeworks is fair game! 1D motion: Reading and understanding x(t), v(t), a(t) graphs, converting between them Constant acceleration problems (fan cart, free fall) Projectile motion: throwing ball into the air, cannon shot off a cliff Vector manipulations: Graphical and algebraic: going from components to angles and magnitudes and vice-versa ngular motion problems slowing down a rotating DVD centripetal acceleration for uniform circular motion Relative motion: relative velocities of two cars at different speeds Physics 211 Spring 2014 Lecture 04-1 10 5
How should I study? Come to office hours (on website!): Work through the practice exam and check your answers against solutions Look over HW solutions Go to physics clinic Work through odd-numbered problems in textbook (solutions are in the back) Especially good in a study group sk questions during your recitation sections Watch parts of videotaped lectures where I work through sample problems Physics 211 Spring 2014 Lecture 04-1 11 Sample Problem: Trebuchet sitting on top of a cliff of height h launches a pumpkin with velocity v 0 at an angle θ. How far does the pumpkin go? What is its speed just before it hits the ground? Physics 211 Spring 2014 Lecture 04-1 12 6
Frame of reference Consider 1D motion of some object Observer at origin of coordinate system measures pair of numbers (x, t) (observer) + coordinate system + clock called frame of reference But we could change the origin and still get the same answer Because observables depend only on Δx Physics 211 Spring 2014 Lecture 04-1 13 Inertial Frames of Reference ny system moving at a constant velocity has a nice inertial frame of reference different frames will perceive velocities differently... But accelerations are still the same That s why things are still nice Physics 211 Spring 2014 Lecture 04-1 14 7
Why bother? Why would we want to use moving frames? nswer: can simplify our analysis of the motion Have no way in principle of knowing whether any given frame is at rest Stolkin is NOT at rest (as we have been assuming!) Physics 211 Spring 2014 Lecture 04-1 15 Reference frame (clock, meterstick) carried along by moving object B Physics 211 Spring 2014 Lecture 04-1 16 8
B B B Physics 211 Spring 2014 Lecture 04-1 17 B B B Physics 211 Spring 2014 Lecture 04-1 18 9
B B B Physics 211 Spring 2014 Lecture 04-1 19 Discussion says: car B moves to right. v B is the velocity of B relative to is. So v B > 0 B says: car moves to left. So, v B < 0 In general, can see that v B = -v B Physics 211 Spring 2014 Lecture 04-1 20 10
Clicker 4-2.1: Otto is in one car, a cameraman is in another. Both cars are going 0.5 m/s to the right. How fast is Otto moving in the camera s frame of reference? (Right is positive!) 1. 0.5 m/s 2. 0 m/s 3. -0.5 m/s 4. 1 m/s 5. None of the above Physics 211 Spring 2014 Lecture 04-1 21 Clicker 4-2.2: Otto is in one car, a cameraman is in another. Otto is going 0.5 m/s to the right. The cameraman is going 1.0 m/s to the right. How fast is Otto moving in the camera s frame of reference? (Right is positive!) 1. 0.5 m/s 2. 0 m/s 3. -0.5 m/s 4. 1 m/s 5. None of the above Physics 211 Spring 2014 Lecture 04-1 22 11
Clicker 4-2.3: Otto is in one car, a cameraman is in another. Otto is going 0.5 m/s to the right. The cameraman is going 0.5 m/s to the left. How fast is Otto moving in the camera s frame of reference? (Right is positive!) 1. -1.0 m/s 2. 0 m/s 3. -0.5 m/s 4. 1.0 m/s 5. None of the above Physics 211 Spring 2014 Lecture 04-1 23 What s more Einstein developed Special theory of relativity to cover situations when velocities approach the speed of light Physics 211 Spring 2014 Lecture 04-1 24 12
Clicker 4-1.5: You are driving East on I-90 at a constant 65 miles per hour. You are passing another car that is going at a constant 60 miles per hour. In your frame of reference (i.e., as measured relative to your car), is the other car 1. going East at constant speed 2. going West at constant speed, 3. going East and slowing down, 4. going West and speeding up. Physics 211 Spring 2014 Lecture 04-1 25 Conclusion If we want to use (inertial) moving frames of reference, then velocities are not the same in different frames However constant velocity motions are always seen as constant velocity There is a simple way to relate velocities measured by different frames. Physics 211 Spring 2014 Lecture 04-1 26 13
Relative Motion in 2D Consider airplane flying in a crosswind velocity of plane relative to air, v P = 240 km/h N wind velocity, air relative to earth, v E = 100 km/h E what is velocity of plane relative to earth, v PE? v PE = v P + v E v E v P v PE Physics 211 Spring 2014 Lecture 04-1 27 cceleration is same for all inertial FOR! We have: v P = v PB + v B For velocity of P measured in frame in terms of velocity measured in B à Δv P /Δt = Δv PB /Δt since v B is constant à Thus acceleration measured in frame or frame B is same! Physics 211 Spring 2014 Lecture 04-1 28 14
Relative Motion in 2D Motion may look quite different in different inertial frames, e.g., ejecting ball from moving cart Cart frame = simple! Earth frame = complicated! Motion of cart Physics 211 Spring 2014 Lecture 04-1 29 ccelerations? We have seen that observers in different inertial frames perceive different velocities Is there something that they do agree on? Demo with ball ejected from cart: cart and Earth observer agree on acceleration (time to fall) Physics 211 Spring 2014 Lecture 04-1 30 15
Reading assignment Forces, Newton s Laws of Motion Ch.5 in textbook Review for Exam 1! Physics 211 Spring 2014 Lecture 04-1 31 16