Chapter 11 Review

Chapter 11 Review - Chapter 11 Lecture Essential University...

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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 right-hand 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_ fit-d" "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 right-hand rule. mg: L!iIL'L'l'IJI'.1|l;:l I'nLul-JK — Torque is compactly iii-111311119... 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 Ill-r 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} {El-3:12;: | _ . 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 three-dimensional 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 E-Piiiiiifijii"i7-i'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;- .- .- -._H_._ ,_ I. IJI _-l' _.- -' _ l-I‘ .. I 1" Non-lng 30m; Fem-q Hour side is clue-or ' II -‘”l'”‘ ""‘3' I - ~ n .3: II. n ."-' 2'? I Inluturc' [ L 1 H | 'r: lll-t.‘ lug-t the. [math 55:1 to:'t|u::_ t' . l I1|J.'-.'|._‘-' curls - H J Illl'llllL'LJ'lli-l I .:'|._' at I . JPN-mt; 7' 'x l- in 1 -_ -' inn: :I'c |1-=.:_':.'. 5': I: '5'. ' Sun Fin‘th ’F‘.“.II"'1“.I flnfirnfin EHIIrI-fii-ifin I‘I'n-I- OIL-In. 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.

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Chapter 11 Review - Chapter 11 Lecture Essential University...

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