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# Download HW8 - Bryn Mawr College

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Transcript

0: 7.3 Ring and bug* A ring m~ss M and radius R lies on its side on a frictionless table. It 1S pivoted to the table at its rim. A bug of mass m walks aro~d the rin~ with speed v, starting at the pivot. What is the rotational velocity of the ring when the bug is . . . (a) halfway around? (b) back at the pivot? :: A ~ ( '2 ~ ) ~ ~r ~ o~- tN b' be "1'.../"'" ~ & ) J;~ I>~ u: U Hvtfu ~! _,k_ wr.J& }?~oI, fu ~./ wr,L '1 L v b, J fZ lAb tNb -.- v br ,>.# .. ~ ¥ 11 YJ 1f(w ~- lP, 'if" :z./L .- ')! u).<lt A- Iilbtrt4: A ~.A Jt..A .1-./ r: '-;"J J yL_ / fk..,. Jn~ 1/- .;-tv.._ A j~ 6 ") tAlrf j Ie iJ) j/dq/ld. rl- 't/" vrJ ' ftv_. yo! -I-w 0 S ~&tI "» ~, I,~ ~c/I-, i ~ ': : ' i jVI.L~ s p.Led ~ hvc& i ~ ttl c> f e. t1~ ~ ~l ~ h ~ l!JcJ,~ I...vv- {",/r>~ vd<u/ly VbJ' ,;d/. f-ILth 1-At' wr: - T 4h 2,/ViR' 21117<7.. wr ~ Awl" b') ~ {.t-<~ ~ - -z, ?Vb 2~ ~ " (1!i. - (~ ~c fk.._._. ('; L J ~J" ~ r &Ur) '-Wr) ~:lI«1 t4A ~ ~~(tA rv-d~ b~ , b '-/n1~ '1. tl... ~ ':Z_~. t.AI/ 'i h1 f2 VJ,:: h/~rf~.: f-"~ VltJ ~ AJ A. ~.J'~~ AH:_ ear on a hill A'3000~lb car is parked on a 30° slope, facing uphill. The center or mass of the caris halfway between the front and rear wheels and.is .2 ft above the ground. The wheels are 8 ft apart. Find the normal force exerted by the road on the front wheels and on the rear wheels. ~./ c ffi N Le 7.11 Wheel and shaft* A wheel is attached to a fixed shaft, and the system is free to rotate without friction. To measure the moment of inertia of the wheelshaft system, a tape of negligible mass wrapped around the shaft is pulled with a known constant force F. When a length L of tape has unwound, the system is rotating with angular speed woo Find the moment of inertia 10 of the system. [J - o LJ; tJ() -L .» -- fl .# I r '- -- B ~. 7.14 A Stick on table* ' . A unif~rul stick of mass M and length I is. suspended horizontally with ~ndB on the edge of a table, and the other end A is held by hand.Point A. As; suddenly released. At the instant after release: (a) What is die. torque around B? (b) Whai is the 'angular acceleration around B? (c)'What is the vertical acceleration of the center of mass? (d)' F.ronl (c), find by inspection the vertical force at B. " :::::t t:: : 1 \3 A "'-) E--. '. b) r c) I M~ -i J 1 _-..--""",,-_........,;_ ,