**Unformatted text preview: **Physics 211
Lecture 14 Today's Concepts:
Rotational Motion
Moment of Inertia Physics 211 Lecture 14, Slide 1
Physics Good prelecture, but just a confusing topic in general.
the moments of solid objects compared to shells and how to calculate each
where do people find massless rods?
I think this actually makes sense.
Should we find the integral each time or just memorize some formulas?
what exactly is moment of inertia, what does that expression actually mean?
I still don't really understand anything with the word angular in it. I think my
brain shuts down a little bit when it comes across that word.
kinetic energy as it relates to rotation.
triple integrals.
Do you guys do sculptures on the side? That system of particles looked like a
piece of modern art.
Heisenberg is out for a drive when he's stopped by a traffic cop. The cop says
'Do you know how fast you were going?' Heisenberg says 'No, but I know
where I am.'
Moment of Inertia calculations!! (also, you should bring back your dog. He could
sit with me and my friends during lecture so he doesn't fall off the counter.
the
However, if he does fall of the counter, you could make that a physics problem
and put it on the test. Example: "If my dog were to run off the table with an initial
velocity of .5 meters/second, how far would he land away from the counter?"
Also, "If students are seated 2 meters away from the counter, would the dog hit
them on his way down?") :-)
Physics 211 Lecture 14, Slide 2
Physics There are about 300 kids in this class, and there are about 5 responses that
are put up on the projection, so i have a 1.67% chance of making it up there.
it
Can i beat the odds?
I am trying to find meaning and purpose in my life and I feel so left out that
left
everyone else has something posted. I tried to be funny, I tried to be stupid, I
to
tried to bribe you, nothing works. I am beginning to feel like a failure at life. :(
failure
I would like to make a genere request for before class. Would it be possible to
request
play a little country for all of them rednecks out there?
how the woman in the T.V show missed the egg throw by so much, no
amount of physics could ever explain that!
I just wanted to take this opportunity to wish my friend Chris LoCasto a happy
happy
19th birthday
Lots of comments like these – can’t show them all
can
Physics 211 Lecture 14, Slide 3
Physics We have exam 2 next Thursday.
In next Wednesdays lecture we will work out HE2 from last
In
semester. Do well on today's clicker questions and we’ll do a rant on
the physics of balloon boy Physics 211 Lecture 14, Slide 4
Physics Summary of Rotations Angular velocity ω is measured in radians/sec
is
Frequency f is measured in revolutions/sec
is
1 revolution = 2π radians
revolution
radians ω = 2πf Period T=1/f
T=1/f 2π
ω=
T
Physics 211 Lecture 14, Slide 5
Physics Another Summary
dω
α=
dt at = Rα v = ωR
v2
ac = = ω 2 R
R ω
Constant α does not mean constant ω
Constant does Act
A disk spins at 2 revolutions/sec. What is its period ? A) T = 2 sec
B) T = 2π sec
C) T = ½ sec Act
A disk spins at 2 revolutions/sec. What is its angular velocity ? A) ω = 2π
π B) ω= C) ω = 4π 2 rad/sec
rad/sec rad/sec Preflight
A wheel which is initially at rest starts to turn with a constant
wheel
angular acceleration. After 4 seconds it has made 4 complete
revolutions.
How many revolutions has it made after 8 seconds?
A) 8
B) 12
C) 16 α Only 43% got this right
so lets try again…
so Physics 211 Lecture 14, Slide 9 …After 4 seconds it has made 4 complete revolutions.
How many revolutions has it made after 8 seconds?
A) 8
B) 12
C) 16
α A) 4 X 2 = 8 ... wow that was tough..
C) theta=1/2 alpha t^2 so doubling t quadruples theta Physics 211 Lecture 14, Slide 10 Calculating Moment of Inertia... Depends on
rotation axis Physics 211 Lecture 14, Slide 11 Preflight
A triangular shape is made from identical balls and
identical rigid, massless rods as shown. The
moment of inertia about the a, b, and c axes is Ia,
Ib, and Ic respectively.
Which of the following orderings is correct?
A) Ia > Ib > Ic
B) Ia > Ic > Ib a C) Ib > Ia > Ic b
c Only 52% got this right
so lets try again…
so
Physics 211 Lecture 14, Slide 12 Which of the following orderings is correct?
A) Ia > Ib > Ic a B) Ia > Ic > Ib b C) Ib > Ia > Ic c A) Ia = 8mr^2 Ib = 3mr^2 Ic = 2mr^2
Ia 8mr^2
3mr^2
2mr^2
B) Ia = 8mr^2 Ib = 3mr^2 Ic = 4mr^2
Ia 8mr^2
3mr^2
4mr^2 Physics 211 Lecture 14, Slide 13 Calculating Moment of Inertia... Bigger when
the mass is
further out Physics 211 Lecture 14, Slide 14 Act In both cases shown below a hula hoop with mass M and
In
radius R is spun with the same angular velocity about a vertical
axis through its center. In Case 1 the plane of the hoop is
axis
parallel to the floor and in Case 2 it is perpendicular.
In which case does the spinning hoop have the most kinetic
energy?
A) Case 1
B) Case 2
C) Same R R
ω Only 46% got this right
so lets try again…
so ω Physics 211 Lecture 14, Slide 15 In which case does the spinning hoop have the most kinetic
In
energy?
A) Case 1
B) Case 2
C) Same R 12
K = Iω
2 R ω
ω
A) The mass is concentrated farther from the axis in Case 1, so it has a
The
higher moment of inertia and, thus, more kinetic energy.
C) The hoop has the same mass, radius, and angular velocity in both
cases, so its kinetic energy will be the same in both cases.
Physics 211 Lecture 14, Slide 16 Act
A mass M is uniformly distributed over the length L of a
thin rod. The mass inside a short element dx is given by:
A) Mdx B)
B) dx
M C)
C) M
dx
L D)
D) L
dx
M x M
L dx Act
A mass M is uniformly distributed over the length L of a
thin rod. The contribution to the rods moment of inertia
provided by element dx is given by:
M
A) x
dx
L
2 1M
B) 2 dx
B)
xL C)
C) M2
dx
L x M
L dx Act
A disk has a radius R. The area of a thin ring inside the
disk with radius r and thickness dr is:
A) πr dr B)
B) 2πrdr 2 r
C)
C) 4πr 3dr
dr Balloon boy physics Physics 211 Lecture 14, Slide 20
Physics ...

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