Welcome back to Physics 211
Today s agenda:
•  Rotations
•  What’s on the exam?
•  Relative motion
Physics 211 – Spring 2014
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ask a physicist
•  Why are neutrinos faster than light
(photons)? I thought light was the
fastest thing around! Also are there any
superluminal speeds?
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Demo: Loop-de-Loop
(need volunteer!)
Draw the components of the
acceleration vector at the sides and
top of the loop-de-loop
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Clicker 4-1.4: What is the acceleration
vector for object speeding up from rest at
point A ?
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Acceleration vectors for object speeding up:
Tangential and radial components
(or parallel and perpendicular)
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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?
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Relating linear and angular kinematics
•  Linear speed: v = (2πr)/T = ω r
•  Radial acceleration: arad = v2/r = ω2r
•  Tangential acceleration: atan = r α
⇥ = ⇥0 + t
⇥ = ⇥0 + ⇤0 t +
⇤ 2 = ⇤02 + 2
Physics 211 – Spring 2014
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t
2
⇥
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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?
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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. A 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 THURSDAY Lecture 04-1 9
Physics 211 – Spring 2014
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
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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
•  Ask questions during your recitation sections
•  Watch parts of videotaped lectures where I work
through sample problems
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Sample Problem:
•  A Trebuchet sitting on top of a cliff of height h launches a
pumpkin with velocity v0 at an angle θ. How far does the
pumpkin go? What is its speed just before it hits the ground?
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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
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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”
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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!)
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Reference frame
(clock, meterstick) carried along by
moving object
B
A
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B
A
B
A
B
A
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B
A
B
A
B
A
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B
A
B
A
B
A
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Discussion
•  A says: car B moves to right. vBA is the
velocity of B relative to A is. So vBA > 0
•  B says: car A moves to left. So, vAB < 0
•  In general, can see that
vAB = -vBA
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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
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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
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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
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What s more …
•  Einstein developed Special theory of
relativity to cover situations when
velocities approach the speed of light
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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.
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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.
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Relative Motion in 2D
•  Consider airplane flying in a crosswind
–  velocity of plane relative to air, vPA = 240 km/h N
–  wind velocity, air relative to earth, vAE = 100 km/h E
–  what is velocity of plane relative to earth, vPE ?
vPE = vPA + vAE
vAE
vPE
vPA
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Acceleration is same for all
inertial FOR!
•  We have:
vPA = vPB + vBA
•  For velocity of P measured in frame A in terms of
velocity measured in B
à ΔvPA/Δt = ΔvPB/Δt since vBA is constant
à Thus acceleration measured in frame A or frame B
is same!
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Relative Motion in 2D
•  Motion may look quite different in
different inertial frames, e.g., ejecting
ball from moving cart
Earth frame
= complicated!
Cart frame
= simple!
Motion of cart
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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)
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Reading assignment
•  Forces, Newton s Laws of Motion
•  Ch.5 in textbook
•  Review for Exam 1 !
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