Welcome back to Physics 211 Today s agenda: Rotations What s on the exam? Relative motion Physics 211 Fall 2012 Lecture 04-1 1
Assignments due this week: Prelecture 4-2: Ch 5.1-5.7 Complete short quiz online before next class HW#4 and SAGE: Due Friday Start studying for the first midterm Physics 211 Fall 2012 Lecture 04-1 2
Relating linear and angular kinematics Linear speed: v = (2πr)/T = ω r Tangential acceleration: a tan = r α Radial acceleration: a rad = v 2 /r = ω 2 r = 0 + t = 0 + 0 t + 1 2 t2 2 = 2 0 +2 Physics 211 Fall 2012 Lecture 04-1 3
Clicker 4-1.1 Rasheed and Sofia are riding a merry-go-round that is spinning steadily. Sofia is twice as far from the axis as is Rasheed. Sofia s angular velocity is that of Rasheed. 1. half 2. the same as 3. twice 4. four times 5. We can t say without knowing their radii. Physics 211 Fall 2012 Lecture 04-1 4 Slide 4-95
Clicker 4-1.2 Rasheed and Sofia are riding a merry-go-round that is spinning steadily. Sofia is twice as far from the axis as is Rasheed. Sofia s speed is that of Rasheed. 1. half 2. the same as 3. twice 4. four times 5. We can t say without knowing their radii. Physics 211 Fall 2012 Lecture 04-1 5 Slide 4-95
Clicker 3-2.10 Rasheed and Sofia are riding a merry-go-round that is spinning steadily. Sofia is twice as far from the axis as is Rasheed. Sofia s acceleration is that of Rasheed. 1. half 2. the same as 3. twice 4. four times 5. We can t say without knowing their radii. Physics 211 Fall 2012 Lecture 04-1 6 Slide 4-95
Sample problem A 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. Assume constant angular acceleration. How many revolutions does the ball make during these 5.0s? Physics 211 Fall 2012 Lecture 04-1 7
Clicker 4-1.4: What is the acceleration vector for object speeding up from rest at point A? Physics 211 Fall 2012 Lecture 04-1 8
What if the speed is changing? Consider acceleration for object on curved path starting from rest Initially, v 2 /r = 0, so no radial acceleration But a is not zero! It must be parallel to velocity Physics 211 Fall 2012 Lecture 04-1 9
Acceleration vectors for object speeding up: Tangential and radial components (or parallel and perpendicular) Physics 211 Fall 2012 Lecture 04-1 10
Demo: Loop-de-Loop Draw the components of the acceleration vector at the sides and top of the loop-de-loop Physics 211 Fall 2012 Lecture 04-1 11
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 Fall 2012 Lecture 04-1 12
Exam 1: Next Tuesday (9/25/11) In Stolkin (here!) at the usual lecture time Material covered: Textbook chapters 1-4 Lectures up through 9/18 (today!) Wed/Fri Workshop activities Homework assignments Work through practice exam problems (posted on website) Work on more practice exam problems in recitation workshop Physics 211 Fall 2012 Lecture 04-1 13
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 Angular 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 Fall 2012 Lecture 04-1 14
How should I study? Come to office hours (also on website!): Manning: Tu 1-2pm, W 3-4pm Catterall: Tues 2-3 pm and Th 2-3pm Work through the practice exam and check your answers against solutions Look over HW solutions (just posted) Go to physics clinic Work through odd-numbered problems in textbook (solutions are in the back) Especially good in a study group Ask questions during your recitation sections Watch parts of videotaped lectures where I work through sample problems Physics 211 Fall 2012 Lecture 04-1 15
Sample Problem: A 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 Fall 2012 Lecture 04-1 16
Sample problem Given the following velocity graph and the information that x(0) = 3, draw the plots of x(t) and a(t). Physics 211 Fall 2012 Lecture 04-1 17
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 Fall 2012 Lecture 04-1 18
Inertial Frames of Reference Any 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 Fall 2012 Lecture 04-1 19
Why bother? Why would we want to use moving frames? Answer: 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 Fall 2012 Lecture 04-1 20
Reference frame (clock, meterstick) carried along by moving object B A Physics 211 Fall 2012 Lecture 04-1 21
B A B A B A Physics 211 Fall 2012 Lecture 04-1 22
B A B A B A Physics 211 Fall 2012 Lecture 04-1 23
B A B A B A Physics 211 Fall 2012 Lecture 04-1 24
Discussion A says: car B moves to right. v BA is the velocity of B relative to A is. So v BA > 0 B says: car A moves to left. So, v AB < 0 In general, can see that v AB = -v BA Physics 211 Fall 2012 Lecture 04-1 25
What s more Einstein developed Special theory of relativity to cover situations when velocities approach the speed of light Physics 211 Fall 2012 Lecture 04-1 26
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 Fall 2012 Lecture 04-1 27
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 Fall 2012 Lecture 04-1 28
Relative Motion in 2D Consider airplane flying in a crosswind velocity of plane relative to air, v PA = 240 km/h N wind velocity, air relative to earth, v AE = 100 km/h E what is velocity of plane relative to earth, v PE? v PE = v PA + v AE v AE v PA v PE Physics 211 Fall 2012 Lecture 04-1 29
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 Fall 2012 Lecture 04-1 30
Accelerations? 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 Fall 2012 Lecture 04-1 31
Acceleration is same for all inertial FOR! We have: v PA = v PB + v BA For velocity of P measured in frame A in terms of velocity measured in B à Δv PA /Δt = Δv PB /Δt since v BA is constant à Thus acceleration measured in frame A or frame B is same! Physics 211 Fall 2012 Lecture 04-1 32
Reading assignment Forces, Newton s Laws of Motion Ch.5 in textbook Review for Exam 1! Physics 211 Fall 2012 Lecture 04-1 33