Chapter 11 Review

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

This preview shows pages 1–7. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

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' ...
View Full Document

## This note was uploaded on 02/12/2012 for the course PHYSICS 104 taught by Professor Staff during the Fall '10 term at Rutgers.

### Page1 / 7

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

This preview shows document pages 1 - 7. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online