Welcome back to Physics 211. Physics 211 Spring 2014 Lecture ask a physicist

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Physics 211 – Spring 2014 Lecture 04-1 1

Welcome back to Physics 211

Today s agenda: •  Rotations

•  What’s on the exam? •  Relative motion

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

Clicker 4-1.4: What is the acceleration

vector for object speeding up from rest at

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Acceleration vectors for object speeding up:

Tangential and radial components

(or parallel and perpendicular)

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)

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Relating linear and angular kinematics

•  Linear speed: v = (2πr)/T = ω r

•  Radial acceleration: a_rad = v2_{/r = ω}2_r

•  Tangential acceleration: a_tan = rα

⇥ = ⇥0+ t

⇥ = ⇥0+ ⇤0t + 1₂ t2 ⇤2 = ⇤₀2+ 2 ⇥

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

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:

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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

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

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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

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!)

Reference frame

(clock, meterstick) carried along by

moving object

A

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Physics 211 – Spring 2014 Lecture 04-1 17 A B A B A B

A B A B A B

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A B A B A B

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

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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

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

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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

What s more …

•  Einstein developed Special theory of

relativity to cover situations when

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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.

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, 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_AE

v_PA vPE

v_PE = v_PA + v_AE

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 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

Cart frame

Earth frame

Motion of cart = simple!

= complicated!

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)

Welcome back to Physics 211. Physics 211 Spring 2014 Lecture ask a physicist