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# 571 Class Note for PHYS 211 at PSU

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COURSE
PROF.
No professor available
TYPE
Class Notes
PAGES
21
WORDS
KARMA
25 ?

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This 21 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at Pennsylvania State University taught by a professor in Fall. Since its upload, it has received 20 views.

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Date Created: 02/06/15
Rotation of a Rigid Body Chapter 11 Rolling Motion Torque Angular Momentum Conservation of Angular Momentum Rolling Motion Rolling without slipping U QKTU b Vcomz zR L df dt v 2 Rd com Kinetic Energy of Rolling Motion from the reference I point P Note from this point of view the wheel undergoes pure rotation no translation Iquot 1 2 0 2v K IPa 2 Parallel Axis Theorem I comMR2 P I K Icom MR2a2 1 1 K Icoma2 MR2a2 2 2 1 1 K Icoma2 Mv2 2 2 com Kinetic Energy of a Rolling Object The kinetic energy of a rolling object is the sum of Kinetic energy of translation of the com Kinetic energy of rotation about the com 1 1 K Icoma2 vaom 2 2 K 2 Km K trans com Example 11 1 See blackboard V Rolling wo Slipping Friction If the wheel is rotation clockwise it also wants to slip however FRIC I ION stops it from slipping V Rolling down an Incline To find the acceleration we use Newton s second LAWS M67 2 Io gt 51 V Yo Yo gsin 90 acom I 1 c0m2 MR 2 F x F Units are N m 239 rFsin 9 Newton s Second Law for Rotation The net torque acting on an object is proportional to the angular acceleration and inversely proportional to the moment of inertia V Angular Momentum I7gtltj5 gt 677me Units are kg mZs or 3 5 m1 3 I7 x 1 5 rp sin 6 1174 11 p redrawn with 3 mil an origin b Example 11 4 Find net angular momentum Angular Momentum and blackboard i I EX frnple 11 5 see bfard 7 1 0 A Angular Momentum and V Igular Velocity gt LIa5 I Conservation of Angular Momentum For a system the total angular s L E I 6 momentum IS the vector sum H If the external torques sum to zero the angular momentum is conserved Rota in x axis a 1 VU 5H8 l unfr L1 1 Lu Initial Final r m Precession of Top dz f dt L Ia dL Mgr dt d dL Mgr dt 1 L Ia 1 Mgr Ia Q preces sional rate Syslenl 39 L quot1 Stale Rolling as Translation and Rotation combined The rolling motion of the wheel is a combination of the pure rotation a and the pure translation b Romlioll axis at I

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