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Unformatted text preview: Chapter 11 Lecture Essential University Physics Richard Wolfson
2nd Edition Rotational Vectors
and Angular Momentum Direction of the Angular Velocity Vector  The direction of angular velocity is given by the
righthand rule. — Curl the fingers of your right hand in the direction of rotation, and your thumb points in the direction of the
angular velocity vector at}. r_ fitd"
"Kb
3"
If
I (S Direction of the Angular Acceleration  Angular acceleration points in the direction of the change in the angular velocity A513 :
a . 55:“: d5:
or = 11111— =—
ar—rﬂ A; d; — The change can be in the same direction as the angular
velocity, increasing the angular speed. — The change can be opposite the angular velocity, decreasing
the angular speed. — Or it can be in an arbitrary direction, changing the direction and
speed as well. Direction of the Torque Vector  The torque vector is perpendicular to both the force vector and the displacement vector from the rotation
axis to the force application point. I — The magnitude of the torque is
r = rFsina — Of the two possible directions
perpendicular to F and F:
the correct direction is given
by the righthand rule. mg: L!iIL'L'l'IJI'.1l;:l I'nLulJK — Torque is compactly iii111311119...
expressed using the vector i' cross product: a... "up w '2. 3t, 'E'I1.*I'::r'lill:'
T : I” X F * thIn'll‘IL'IoI:11~.
I" [out ot'pzigej in Illr LIIr': Angular Momentum  For a single particle, angular momentum E is a vector
given by the cross product of the displacement vector
from the rotation axis with the linear momentum of the
particle: —Ir LzFxﬁ — For the case of a particle in a
circular path, L = mvr, and If is
upward, perpendicular to the
circle. a" is puipuiuliuulnr' ii] I". — For sufficiently symmetric objects, L is the product of rotational inertia and angular
velocity: — 12:15) Newton’s Law and Angular Momentum  In terms of angular momentum, the rotational analog of
Newton’s second law is a 1?:—
dr — Therefore a system’s angular momentum changes only if
there's a non—zero net torque acting on the system. — If the net torque is zero, then angular momentum is
conserved. ' Changes in rotational inertia then result in changes in angular speed: %
FE? I: 'II I'IIIIF 'I.I .".'.':~.a l IIIH:'I 1LI The skaters angular momentum aﬁﬁ} {El3:12;:
 _ . L {as is conserved, so her angular P. ,I
J «1% 1.4.. speed increases when she i i 
'. T reduces her rotational inertia. W“ .:g_‘ ." an .I rr. I'I.
'l\\:’ l. x f CL & {in Precession  Precession is a threedimensional phenomenon
involving rotational motion. — Precession occurs when a torque acts on a rotating
object, changing the direction but not the magnitude of its
angular momentum vector. — As a result the rotation axis undergoes circular motion: Precessmn Of a gymscﬂpe Precession slowly changes
EPiiiiiiﬁjii"i7i'f.Tili.’?'_‘i‘l‘ipgftfip the direction of Earths rotation axis
LI;~..i{i'm:'..nit“ . . 'l'nniue Cannes “Kira [Ll ['II'L‘L'z‘H‘L '. .
.
1;
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.
._H_._
,_ I. IJI _l' _. ' _
lI‘
.. I 1" Nonlng 30m; Femq Hour side is clueor
' II ‘”l'”‘ ""‘3' I  ~ n .3: II. n ."' 2'? I Inluturc' [ L 1 H  'r:
lllt.‘ lugt the. [math 55:1
to:'tu::_ t' . l I1J.'.'._‘' curls  H J Illl'llllL'LJ'llil I .:'._' at I . JPNmt; 7' 'x l in 1 _ ' inn: :I'c 1=.:_':.'. 5': I: '5'. ' Sun
Fin‘th ’F‘.“.II"'1“.I ﬂnﬁrnﬁn EHIIrIﬁiiﬁn I‘I'nI OILIn. I14 I' ...
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This note was uploaded on 02/12/2012 for the course PHYSICS 104 taught by Professor Staff during the Fall '10 term at Rutgers.
 Fall '10
 Staff
 Physics

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