This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: 1. A very thin sheet has a mass density a = 720333;, where C is a positive constant. It lies in
the m—y plane and its sides are both of length a. (a) Determine the inertia tensor for the plane. (b) What are the principal moments of inertia? It? 1 Sf 55'5“ka ‘ Yixcl'
a
In  SOZCLJ)(3L+%) AKAJ  ”HQ 37%;: _ ‘ica‘
IL '—‘ —  I .5: ’_ , { ._.
I 382033) K7 Axel) 71c 31  {E L, [:3 : SQ'KJQDX? 1‘: it} 1. $910.13) i)? ﬁbeokj ‘ f)
[33 2 SGLCkJ\ Ck‘fjB Akdj :. 72 Q (—53%: Jr 352; 2:3) : {90.5“
I 2 ”\Ca‘ ..ch.‘ o v 6 CAL; $0 a,‘ b O o 13503 ‘1—1 0 _ _ 1
ca‘ 6 By. :9 0" IX“ ”I” “‘0
g (H D LIL—1y a? I%14—'L1"3
° 0 lirl
Qe—‘QCI’PIXI—I)
=7 I: 1, 19,11 2. A projectile is shot from a latitude A as shown below. Its initial velocity is 110 due south,
and its angle relative to the local horizontal is 45° as shown below. Because of the Earth’s rotation, the projectile appears to deviate from its original path. Let the Earth’s angular
velocity be u). (a) As a. function of time (t) determine the component of the projectile’s velocity that results
from the Coriolis effect. Hint: Project all vectors onto the :17 and y axes as shown. (is) Determine how far the particle appears to deviate from its original path as a function of
t. A
F; = —2m\23“\!
L3: "‘ LDC05X? togAXE}
V 3’
Va Cote; r} Vbs\inOJA ~86§
‘ V0
45° “ :1 ‘1‘
F: 3' Zm VDCMB vD smeﬁt a
‘UCDJX wSinX (3 ~ A
E: lmi VOCJeusink + UC05\(V931A6*5'tjjz A . )4
a: %  26/0 casewsink { gco>\&65‘h3—3f) '3 V?— fjvocosaws‘mXé + 2% Sin Qucoaké
_. Cu coaxsfii‘ ML! CzD Slﬂtt 411". h m.» Conrail:
b\ V: €531 Q’QL Ohm ’“tk TMLLLc 73%;,
6 73‘) f 7' [Vgu (C056 Slnx 4 SiA9C03}3€L .. (.1605). .6319?
/—”}’§”’ 7 if 3. A body has an inertia tensor given by: 2Mb2 0 0
0 5Mb2 3Mb2
0 {5sz 511/1322 where b is a positive constant. The body rotates about the vertical axis with an angular frequency w. The angle between the vertical and the symmetry axis of the body is as, where
the origin is located at the intersection of the principal axes. (a) Find the principal moments of inertia for this system.
(b) Determine the angular momentum about the origin in the body frame. (0) What is the magnitude and direction of the torque in the inertial frame. Zi'vul)1L ’f_ <3 C)
o grub: 3my¢l —_ o
o 3"“34. S'n Ltl ﬁgmbt—llli SIMS13'“ ~ and?) lo
.. Um51"1)(28‘h§b"  lumbt‘IL— qmg‘]: a
x (my 'I)( 8mL  LXML‘il .. 1.
Tu “: 11.1.: Zmz’t 1:13" ﬁrm; A 3N2" *UC§\r~°L
L 2
ZmbL b
6M5." +mu3°L
ﬁx:  2mbluslni La?“ ’4'“ imbtu‘JM'L m... Carw E
'A
" (“' Ug‘mr’t; '4' MCQJé‘X 'Zmlzu$l\qoi’\\c }— ﬁmllwcoso'la) 2 r' E gmll UL S‘IOJCD3‘! ’i‘ ZMBI “153‘“06565‘13 ': ...
View
Full Document
 Spring '08
 none

Click to edit the document details