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Advanced Rotational Dynamics for AP Physics

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Advanced Rotational Dynamics for AP Physics +Common Examples of Rotation +Review of Introductory Rotational Dynamics +Combined translation and rotation – PowerPoint PPT presentation

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Title: Advanced Rotational Dynamics for AP Physics


1
Advanced Rotational Dynamicsfor AP Physics
  • Common Examples of Rotation
  • Review of Introductory Rotational Dynamics
  • Combined translation and rotation
  • Rolling without slipping
  • Rolling with slipping
  • Rotational form of Conservation Laws
  • Collisions involving objects having Moment of
    Inertia

2
Advanced Rotational Dynamicsfor AP Physics
  • Common Examples of Rotation
  • Review of Introductory Rotational Dynamics
  • Combined translation and rotation
  • Rolling without slipping
  • Rolling with slipping
  • Rotational form of Conservation Laws
  • Collisions involving objects having Moment of
    Inertia

3
Advanced Rotational Dynamicsfor AP Physics
  • Common Examples of Rotation
  • Review of Introductory Rotational Dynamics
  • Combined translation and rotation
  • Rolling without slipping
  • Rolling with slipping
  • Rotational form of Conservation Laws
  • Collisions involving objects having Moment of
    Inertia

4
Advanced Rotational Dynamicsfor AP Physics
  • Common Examples of Rotation
  • Review of Introductory Rotational Dynamics
  • Combined translation and rotation
  • Rolling without slipping
  • Rolling with slipping
  • Rotational form of Conservation Laws
  • Collisions involving objects having Moment of
    Inertia

5
Examples of rotation Earth
  • To find the direction of omega, apply the right
    hand rule as follows
  • With fingers curling in direction of rotation,
    the thumb gives direction of omega
  • i.e. direction of earths omega is upward

6
rotation of the sky
  • star trails
  • centered on Polaris
  • rotate once a day

7
rotation can be fun
8
sometimes the goal is rotational equilibrium
  • 1st condition for equilibrium
  • Fnet 0
  • 2nd condition for equilbrium
  • torque net 0
  • i.e., torque ccw torque cw

9
rotational equilibrium again
10
sometimes the goal is large rotational velocity
11
M31 rotates once every few hundred million years
12
Katrina rotated
13
a generic kidney shaped object rotates about a
fixed axisa thing of beauty is a joy forever!
14
a turbine (driven by moving fluid) rotates about
a fixed axis
15
a jet engine rotates about a fixed axis
16
(No Transcript)
17
steam driven power plant turbineimagine this
thing rotating at 60 hzgenerating your
electricity
18
electric motors are backwards connected
generatorsthey are still mechanical rotators
about a fixed axis
19
electric motors power our elderly friends
scooters
20
and nuclear subs also(when they are submerged)
21
gears rotate about a fixed axis
22
gear attached to an electric motor(sounds like a
good idea to me)
23
nanotechology electric motor gear (the gear
teeth are smaller than a red blood cell)rotating
about a fixed axis, imaged with an electron
microscope(end of examples of rotation)
24
Advanced Rotational Dynamicsfor AP Physics
  • Examples of Rotation
  • Review of Introductory Rotational Dynamics
  • Combined translation and rotation
  • Rolling without slipping
  • Rolling with slipping
  • Rotational form of Conservation Laws
  • Collisions involving objects having Moment of
    Inertia

25
Advanced Rotational Dynamicsfor AP Physics
  • Examples of Rotation
  • Review of Introductory Rotational Dynamics
  • Combined translation and rotation
  • Rolling without slipping
  • Rolling with slipping
  • Rotational form of Conservation Laws
  • Collisions involving objects having Moment of
    Inertia

26
Advanced Rotational Dynamicsfor AP Physics
  • Examples of Rotation
  • Review of Introductory Rotational Dynamics
  • Combined translation and rotation
  • Rolling without slipping
  • Rolling with slipping
  • Rotational form of Conservation Laws
  • Collisions involving objects having Moment of
    Inertia

27
Rotational Kinematics
  • T angular position wrt arbitrary origin
  • ?? angular displacement (rad)
  • ? ?? / ?t d? / dt (rad/s)
  • a ? ? / ?t d ? / dt d2? / dt2
    (rad/s2)
  • s r ?
  • v r ?
  • a r a

28
a constant implies
  • ?? ?0t ½ at2
  • ? ?0 a t
  • ?2 ?02 2 a ??
  • ?? ½ (?0 ?) t
  • If a is variable, you need calculus

29
Intro Rotational Dynamics
  • ? t r x F
  • I S mi ri2 (collection of point masses)
  • ? r2 dm (continuous matter distribution)
  • I total I 1 I 2 I 3 (composite
    object)
  • Fnet ma becomes ?net tnet I a

30
Advanced Rotational Dynamicsfor AP Physics
  • Common Examples of Rotation
  • Review of Introductory Rotational Dynamics
  • Combined translation and rotation
  • Rolling without slipping
  • Rolling with slipping
  • Rotational form of Conservation Laws
  • Collisions involving objects having Moment of
    Inertia

31
Advanced Rotational Dynamicsfor AP Physics
  • Common Examples of Rotation
  • Review of Introductory Rotational Dynamics
  • Combined translation and rotation
  • Rolling without slipping
  • Rolling with slipping
  • Rotational form of Conservation Laws
  • Collisions involving objects having Moment of
    Inertia

32
Advanced Rotational Dynamicsfor AP Physics
  • Common Examples of Rotation
  • Review of Introductory Rotational Dynamics
  • Combined translation and rotation
  • Rolling without slipping
  • Rolling with slipping
  • Rotational form of Conservation Laws
  • Collisions involving objects having Moment of
    Inertia

33
Earth revolves (translation of cm) and rotates
about cm
34
Look Ma, no hands
35
combined translation and rotation
  • Ktotal Ktranslational Krotational
  • Kof the cm Karound the cm
  • ½ mv2 ½ I ?2

36
Advanced Rotational Dynamicsfor AP Physics
  • Common Examples of Rotation
  • Review of Introductory Rotational Dynamics
  • Combined translation and rotation
  • Rolling without slipping
  • Rolling with slipping
  • Rotational form of Conservation Laws
  • Collisions involving objects having Moment of
    Inertia

37
Advanced Rotational Dynamicsfor AP Physics
  • Common Examples of Rotation
  • Review of Introductory Rotational Dynamics
  • Combined translation and rotation
  • Rolling without slipping
  • Rolling with slipping
  • Rotational form of Conservation Laws
  • Collisions involving objects having Moment of
    Inertia

38
Advanced Rotational Dynamicsfor AP Physics
  • Common Examples of Rotation
  • Review of Introductory Rotational Dynamics
  • Combined translation and rotation
  • Rolling without slipping
  • Rolling with slipping
  • Rotational form of Conservation Laws
  • Collisions involving objects having Moment of
    Inertia

39
linear and angular velocity and acceleration are
proportional
40
rolling without slipping in our golden years
41
rolling without slipping
  • v ? r (use with energy conservation)
  • atangential a r (use with 2nd laws)
  • friction acts, but does no work
  • energy conserved as Wnc 0

42
Advanced Rotational Dynamicsfor AP Physics
  • Common Examples of Rotation
  • Review of Introductory Rotational Dynamics
  • Combined translation and rotation
  • Rolling without slipping (pure rolling)
  • Rolling with slipping
  • Rotational form of Conservation Laws
  • Collisions involving objects having Moment of
    Inertia

43
Advanced Rotational Dynamicsfor AP Physics
  • Common Examples of Rotation
  • Review of Introductory Rotational Dynamics
  • Combined translation and rotation
  • Rolling without slipping (pure rolling)
  • Rolling with slipping
  • Rotational form of Conservation Laws
  • Collisions involving objects having Moment of
    Inertia

44
Advanced Rotational Dynamicsfor AP Physics
  • Common Examples of Rotation
  • Review of Introductory Rotational Dynamics
  • Combined translation and rotation
  • Rolling without slipping (pure rolling)
  • Rolling with slipping
  • Rotational form of Conservation Laws
  • Collisions involving objects having Moment of
    Inertia

45
linear and angular velocities and accelerations
are independent,i.e., hes not getting very much
bang (v) for his buck (?)
46
dont try this at home
47
rolling with slipping
  • v ? ? r
  • atangential ? a r
  • apply Fnet ma to find atangential of the cm
  • apply ?net Ia to find a around the cm
  • to compute t where pure rolling sets in,
  • set a(t) a(t) r, where a(t) and a(t) are
  • solutions of force and torque equations

48
Advanced Rotational Dynamicsfor AP Physics
  • Common Examples of Rotation
  • Review of Introductory Rotational Dynamics
  • Combined translation and rotation
  • Rolling without slipping
  • Rolling with slipping
  • Rotational form of Conservation Laws
  • Collisions involving objects having Moment of
    Inertia

49
Advanced Rotational Dynamicsfor AP Physics
  • Common Examples of Rotation
  • Review of Introductory Rotational Dynamics
  • Combined translation and rotation
  • Rolling without slipping
  • Rolling with slipping
  • Rotational form of Conservation Laws
  • Collisions involving objects having Moment of
    Inertia

50
Advanced Rotational Dynamicsfor AP Physics
  • Common Examples of Rotation
  • Review of Introductory Rotational Dynamics
  • Combined translation and rotation
  • Rolling without slipping
  • Rolling with slipping
  • Rotational form of Conservation Laws
  • Collisions involving objects having Moment of
    Inertia

51
definition of angular momentum
  • L r x p r x mv (point m moving at v)
  • L I ? (rigid body with moment I)

52
law of motion in terms of L
  • torque net ?L/ ?t dL / dt

53
Conservation of angular momentum
  • if torque net 0, then dL / dt 0
  • and so, L constant
  • so, I initial ? initial I final ? final
  • (ice skater)

54
easier said than done
55
The agony of defeat(net torque ? 0, L not
conserved)
56
The thrill of victory(net torque 0, L
conserved)
57
Conservation of energy, including rotation
  • Simply allow for rotational
  • as well as translational K

58
Conservation of linear momentum
  • is not affected by rotational motion, but
    applies to the cm of the body as before
  • (i.e., if Fnet,ext 0 on system. That is,
  • if something is nailed down and rotates,
    linear momentum is not conserved, but L can be)

59
Advanced Rotational Dynamicsfor AP Physics
  • Common Examples of Rotation
  • Review of Introductory Rotational Dynamics
  • Combined translation and rotation
  • Rolling without slipping
  • Rolling with slipping
  • Rotational form of Conservation Laws
  • Collisions involving objects having Moment of
    Inertia

60
Advanced Rotational Dynamicsfor AP Physics
  • Common Examples of Rotation
  • Review of Introductory Rotational Dynamics
  • Combined translation and rotation
  • Rolling without slipping
  • Rolling with slipping
  • Rotational form of Conservation Laws
  • Collisions involving objects having Moment of
    Inertia

61
Advanced Rotational Dynamicsfor AP Physics
  • Common Examples of Rotation
  • Review of Introductory Rotational Dynamics
  • Combined translation and rotation
  • Rolling without slipping
  • Rolling with slipping
  • Rotational form of Conservation Laws
  • Collisions involving objects having Moment of
    Inertia

62
Advanced Rotational Dynamicsfor AP Physics
  • Common Examples of Rotation
  • Review of Introductory Rotational Dynamics
  • Combined translation and rotation
  • Rolling without slipping
  • Rolling with slipping
  • Rotational form of Conservation Laws
  • Collisions (and other systems) involving objects
    having Moment of Inertia

63
  • this is rather important on the AP Exam

64
  • Unfortunately, few common practical applications
    exist for this type of problem.
  • They are simply artificially contrived

65
Any or all 3 conservation laws of energy, linear
momentum, and angular momentum may be
satisfied!You have to figure out which ones are
operating, if they dont tell you!
  • If Wnc 0, then Einitial Efinal
  • If Fnet,ext 0, then pinitial pfinal
  • If ?net 0, then Linitial Lfinal

66
The End
  • Thats it! Now go make a 5!
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