Welcome back to Physics 215 Todays agenda Motion
Welcome back to Physics 215 Today’s agenda • Motion along curved paths, circles • Tangential and radial components of acceleration • Rotations • Introduction to relative motion Physics 215 – Fall 2014 Lecture 03 -2 1
Current homework assignment HW 3: – Exam-style problem (print out from course website) – Ch. 4 (Knight textbook): 52, 62, 80, 84 – due Wednesday, Sept 17 th in recitation Physics 215 – Fall 2014 Lecture 03 -2 2
Exam 1: next Thursday (9/18/14) • In room 208 (here!) at the usual lecture time • Material covered: – Textbook chapters 1 - 4 – Lectures up through 9/16 (slides online) – Wed/Fri Workshop activities – Homework assignments • Exam is closed book, but you may bring calculator and one handwritten 8. 5” x 11” sheet of notes. • Work through practice exam problems (posted on website) • Work on more practice exam problems next Wednesday in recitation workshop Physics 215 – Fall 2014 Lecture 03 -2 3
Acceleration vector for object speeding up from rest at point A ? Physics 215 – Fall 2014 Lecture 03 -2 4
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 215 – Fall 2014 Lecture 03 -2 5
Acceleration vectors for object speeding up: Tangential and radial components (or parallel and perpendicular) Physics 215 – Fall 2014 Lecture 03 -2 6
Sample problem A Ferris wheel with diameter 14. 0 m, which rotates counter-clockwise, is just starting up. At a given instant, a passenger on the rim of the wheel and passing through the lowest point of his circular motion is moving at 3. 00 m/s and is gaining speed at a rate of 0. 500 m/s 2. (a) Find the magnitude and the direction of the passenger’s acceleration at this instant. (b) Sketch the Ferris wheel and passenger showing his velocity and acceleration vectors. Physics 215 – Fall 2014 Lecture 03 -2 7
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 215 – Fall 2014 Lecture 03 -2 8
Ball going through loop-the-loop Physics 215 – Fall 2014 Lecture 03 -2 9
Rotations about fixed axis • Linear speed: v = (2 pr)/T = r. Quantity is called angular velocity • is a vector! Use right hand rule to find direction of . • Angular acceleration a = Dw/Dt is also a vector! – and parallel angular speed increasing – and antiparallel angular speed decreasing Physics 215 – Fall 2014 Lecture 03 -2 10
A disk is rotating at a constant rate about a vertical axis through its center. Point Q is twice as far from the center as point P. The angular velocity of Q is 1. 2. 3. 4. twice as big as P the same as P half as big as P none of the above Physics 215 – Fall 2014 Lecture 03 -2 11
A disk is rotating at a constant rate about a vertical axis through its center. Point Q is twice as far from the center as point P. The linear velocity of Q is 1. 2. 3. 4. twice as big as P the same as P half as big as P none of the above Physics 215 – Fall 2014 Lecture 03 -2 12
Relating linear and angular kinematics • Linear speed: v = (2 pr)/T = r • Tangential acceleration: atan = r • Radial acceleration: arad = v 2/r = 2 r Physics 215 – Fall 2014 Lecture 03 -2 13
Problem – slowing a DVD I = 27. 5 rad/s, = -10. 0 rad/s 2. • how many revolutions per second? 10. 0 cm • linear speed of point on rim? • angular velocity at t = 0. 30 s ? • when will it stop? Physics 215 – Fall 2014 Lecture 03 -2 14
Kinematics • Consider 1 D motion of some object • Observer at origin of coordinate system measures pair of numbers (x, t) – (observer) + coordinate system + clock called frame of reference • (x, t) not unique – different choice of origin changes x (no unique clock. . . ) Physics 215 – Fall 2014 Lecture 03 -2 15
Change origin? • Physical laws involve velocities and accelerations which only depend on Dx • Clearly any frame of reference (FOR) with different origin will measure same Dx, v, a, etc. Physics 215 – Fall 2014 Lecture 03 -2 16
Inertial Frames of Reference • Actually can widen definition of FOR to include coordinate systems moving at constant velocity • Now different frames will perceive velocities differently. . . • Accelerations? Physics 215 – Fall 2014 Lecture 03 -2 17
Moving Observer • Often convenient to associate a frame of reference with a moving object. • Can then talk about how some physical event would be viewed by an observer associated with the moving object. Physics 215 – Fall 2014 Lecture 03 -2 18
Reference frame (clock, meterstick) carried along by moving object B A Physics 215 – Fall 2014 Lecture 03 -2 19
B A B A Physics 215 – Fall 2014 Lecture 03 -2 20
B A B A Physics 215 – Fall 2014 Lecture 03 -2 21
B A B A Physics 215 – Fall 2014 Lecture 03 -2 22
Discussion • From point of view of A, car B moves to right. We say the velocity of B relative to A is v. BA. Here v. BA > 0 • But from point of view of B, car A moves to left. In fact, v. AB < 0 • In general, can see that v. AB = -v. BA Physics 215 – Fall 2014 Lecture 03 -2 23
Galilean transformation y. A y. B v. BA P v. BAt x. B x. A x. PA = x. PB + v. BAt -- transformation of coordinates Dx. PA/Dt = Dx. PB/Dt + v. BA v. PA = v. PB + v. BA -- transformation of velocities Physics 215 – Fall 2014 Lecture 03 -2 24
Discussion • Notice: – It follows that v. AB = -v. BA – Two objects a and b moving with respect to, say, Earth then find (P a, B b, A E) vab = va. E - vb. E Physics 215 – Fall 2014 Lecture 03 -2 25
Reading assignment • Relative motion • 4. 4 in textbook • Review for Exam 1 ! Physics 215 – Fall 2014 Lecture 03 -2 26
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