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Physics 215 – Fall 2014Lecture Exam 1: next Thursday (9/18/14) In room 208 (here!) at the usual lecture time Material covered: –Textbook chapters –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
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Physics 215 – Fall 2014 Lecture 03-2 1
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 2
Current homework assignment
HW3:– Exam-style problem (print out from course website)– Ch.4 (Knight textbook): 52, 62, 80, 84– due Wednesday, Sept 17th in recitation
Physics 215 – Fall 2014 Lecture 03-2 3
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 4
Acceleration vector for object speeding up from rest at point A ?
Physics 215 – Fall 2014 Lecture 03-2 5
What if the speed is changing?• Consider acceleration for object on curved
path starting from rest
• Initially, v2/r = 0, so no radial acceleration
• But a is not zero! It must be parallel to velocity
Physics 215 – Fall 2014 Lecture 03-2 6
Acceleration vectors for object speeding up:
Tangential and radial components
(or parallel and perpendicular)
Physics 215 – Fall 2014 Lecture 03-2 7
Sample problemA 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/s2. (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 8
SummaryComponents 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 9
Ball going through loop-the-loop
Physics 215 – Fall 2014 Lecture 03-2 10
Rotations about fixed axis• Linear speed: v = (2r)/T = r.
Quantity is called angular velocity
is a vector! Use right hand rule to find direction of .
• Angular acceleration t is also a vector! and parallel angular speed
increasing and antiparallel angular
speed decreasing
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 angular velocity of Q is
1. twice as big as P2. the same as P3. half as big as P4. none of the above
Physics 215 – Fall 2014 Lecture 03-2 12
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. twice as big as P2. the same as P3. half as big as P4. none of the above
Physics 215 – Fall 2014 Lecture 03-2 13
Relating linear and angular kinematics• Linear speed: v = (2r)/T = r
• Tangential acceleration: atan = r
• Radial acceleration: arad = v2/r = 2r
Physics 215 – Fall 2014 Lecture 03-2 14
Problem – slowing a DVD I = 27.5 rad/s, = -10.0 rad/s2
• how many revolutions per second?
• linear speed of point on rim?
• angular velocity at t = 0.30 s ?
• when will it stop?
10.0 cm
.
Physics 215 – Fall 2014 Lecture 03-2 15
Kinematics• 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
• (x, t) not unique – different choice of origin changes x (no unique clock...)
Physics 215 – Fall 2014 Lecture 03-2 16
Change origin?
• Physical laws involve velocities and accelerations which only depend on x
• Clearly any frame of reference (FOR) with different origin will measure same x, v, a, etc.
Physics 215 – Fall 2014 Lecture 03-2 17
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 18
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 19
Reference frame
(clock, meterstick) carried along by moving object
A
B
Physics 215 – Fall 2014 Lecture 03-2 20
A
B
A
B
A
B
Physics 215 – Fall 2014 Lecture 03-2 21
A
B
A
B
A
B
Physics 215 – Fall 2014 Lecture 03-2 22
A
B
A
B
A
B
Physics 215 – Fall 2014 Lecture 03-2 23
Discussion• From point of view of A, car B moves to
right. We say the velocity of B relative to A is vBA. Here vBA > 0
• But from point of view of B, car A moves to left. In fact, vAB < 0
• In general, can see that vAB = -vBA
Physics 215 – Fall 2014 Lecture 03-2 24
Galilean transformation
xA
xB
vBA
P
vBAt
xPA = xPB + vBAt -- transformation of coordinates
xPAt xPB/t + vBA
vPA = vPB + vBA -- transformation of velocities
yByA
Physics 215 – Fall 2014 Lecture 03-2 25
Discussion
• Notice:– It follows that vAB = -vBA
– Two objects a and b moving with respect to, say, Earth then find (Pa, Bb, AE)
vab = vaE - vbE
Physics 215 – Fall 2014 Lecture 03-2 26
Reading assignment
• Relative motion
• 4.4 in textbook
• Review for Exam 1 !