Phys 2101 Gabriela González. cos. sin. sin

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Bertram Ethelbert Weaver
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1 1 Phys 101 Gabiela González a m t t ma ma m m T α φ ω φ sin cos α τ α φ τ sin m m α τ I

2 We know all of that aleady!! 3 The figue shows the massive shield doo at a neuton test facility at Lawence Livemoe Laboatoy; this is the wold's heaviest hinged doo. The doo has a mass of 44,000 kg, a otational inetia about a vetical axis though its huge hinges of 8.7x10 4 kg m, and a (font) face width of.4 m. Neglecting fiction, what steady foce, applied at its oute edge and pependicula to the plane of the doo, can move it fom est though an angle of 90 in 30 s? 4

3 In the figue, a block has mass M 500 g, the othe has mass m 460 g, and the pulley, which is mounted in hoizontal fictionless beaings, has a adius of 5.00 cm. When eleased fom est, the heavie block falls 75.0 cm in 5.00 s (without the cod slipping on the pulley). (a) What is the magnitude of the blocks' acceleation? What is the tension in the pat of the cod that suppots (b) the heavie block and (c) the lighte block? (d) What is the magnitude of the pulley's angula acceleation? (e) What is its otational inetia? 5 (a) What is the magnitude of the blocks' acceleation? y 1 at a y /t 0.75m /5s 0.06m /s What is the tension in the pat of the cod that suppots (b) the heavie block and Mg T 1 Ma T 1 M(a + g) 0.5kg 9.86m /s 4.93N (c) the lighte block? T mg ma T m(a g) 0.496kg 9.794m /s 4.86N (Tensions ae not equal any moe!!!) (d) What is the magnitude of the pulley's angula acceleation? α a /R 0.06m /s /0.05m 1.ad /s (e) What is its otational inetia? τ T 1 R + T R Iα I (T T 1 )R /α 0.07N 0.05m /1.ad /s 0.009kgm 6 3

4 A mete stick is held vetically with one end on the floo and is then allowed to fall. Assuming that the end on the floo does not slip (a) What foces ae acting on the stick? (b) What foces ae doing wok? (c) ind the speed of the othe end when it hits the floo. 7 A mete stick is held vetically with one end on the floo and is then allowed to fall. Assuming that the end on the floo does not slip (a) What foces ae acting on the stick? Gavity (at the cente of mass), static fiction and nomal foce (at bottom end) (b) What foces ae doing wok? Only gavity does (positive) wok. (c) ind the speed of the othe end when it hits the floo. The motion is pue otation about the lowe end. Use consevation of enegy: I bot I com + M(L /) 1 1 ML ML 1 3 ML 1 I botω Mg L 0 ω MgL 3 g I bot L v top ωl 3gL 5.4 m/s 8 4

5 Assume a 50 kg woman is in a oto, with µ s 0.5, Rm. What s the minimum angula velocity that will let the woman be stuck to the wall without a floo? 9 Assume a 50 kg woman is in a oto, with µ s 0.5, Rm. What s the minimum angula velocity that will let the woman be stuck to the wall without a floo? We need enough static fiction to cancel gavity. Maximum value of static fiction is µ s N. The nomal foce is the centipetal foce, o mω R. mg µ s N µ s mω R ω g/(µ s R) 3.13 ad/s ~ 30 pm Answe is independent of the mass, but vey much dependent on coefficient of fiction! 10 5

6 11 It depends on the efeence fame! If we sit at the cente of the wheel If we sit on the oad, following the bike 1 6

7 KE ω I com Mv com 13 A solid ball stats fom est at the uppe end of the tack shown in the figue, and olls without slipping until it olls off the ight-hand end. If H 6.0 m and h.0 m and the tack is hoizontal at the ight-hand end, how fa hoizontally fom point A does the ball land on the floo? 14 7

8 A solid ball stats fom est at the uppe end of the tack shown in the figue, and olls without slipping until it olls off the ight-hand end. If H 6.0 m and h.0 m and the tack is hoizontal at the ight-hand end, how fa hoizontally fom point A does the ball land on the floo? om H to h: use consevation of enegy to get speed. Notice that kinetic enegy has both tanslational and otational components: ΔK + ΔU 0 1 mv com + 1 I comω mg(h h) 0 1 mv com + 1 v com 5 mr mg(h h) R 7 10 mv com mg(h h) v com (10/7)g(H h) 7.48 m/s Notice that this is a smalle velocity than a point mass: olling bodies fall slowe than point masses, and the lage the otational inetia, the slowe they fall). The velocity of the cente of mass at h is hoizontal. om h on, com motion is a pojectile motion (and the ball keeps otating, but with a constant angula velocity, since gavity does not poduce a toque) h 1 gt t h /g 0.64 s x vt 4.78 m 15 No slipping! iction is static; and does no wok. Thee is a net foce, so the cente of mass is acceleated. If the cente of mass is acceleated, thee is also angula acceleation. net m a com τ Icom α net a com Mgsinθ f s Ma com R f s I com α I com a com /R gsinθ 1+ I com /R 16 8

9 A constant hoizontal foce of magnitude 10 N is applied to a wheel of mass 10 kg and adius 0.30 m as shown in the figue. The wheel olls smoothly on the hoizontal suface, and the acceleation of its cente of mass has magnitude 0.60 m/s. (a) What ae the magnitude and diection of the fictional foce on the wheel? (b) What is the otational inetia of the wheel about the otation axis though its cente of mass? 17 A constant hoizontal foce of magnitude 10 N is applied to a wheel of mass 10 kg and adius 0.30 m as shown in the figue. The wheel olls smoothly on the hoizontal suface, and the acceleation of its cente of mass has magnitude 0.60 m/s. (a) What ae the magnitude and diection of the fictional foce on the wheel? net ma f s ma com f s ma com 4N (b) What is the otational inetia of the wheel about the otation axis though its cente of mass? τ net Iα f s R Ia com /R I f s R /a com 0.6kgm 18 9

12. Rolling, Torque, and Angular Momentum

12. Rolling, Torque, and Angular Momentum 12. olling, Toque, and Angula Momentum 1 olling Motion: A motion that is a combination of otational and tanslational motion, e.g. a wheel olling down the oad. Will only conside olling with out slipping.