Question

Each of the gears A and B has a mass of 1.6 kg and a radius of gyration of 60 mm, while gear C has a mass of 12 kg and a radius of gyration of 150 mm. A couple M of constant magnitude 10 N·m is applied to gear C. Determine the number of revolutions of gear C required for its angular velocity to increase from 100 to 450 rpm and the corresponding tangential force acting on gear A. (Round the final answers to two decimal places.) SO mm Somm 200 mm 5.7 rev. The number of revolutions of gear C required for its angular velocity to increase from 100 to 450 rpm is The corresponding tangential force acting on gear A is 9.9 N.

Answer 1

Iet A %adius of the geor A Va = Tadius oS the *eat B adius of the gear A, and we arguar velocity of esbectve kinematics of the sastem ves a e -he gea A, B and Now the SAA 30 A 30wg 20owc WA- B2.5wc Initkal angulas velocit of gex is (Cue) 2 T 10. 472 ad/s Fnal ongolar velocity of ges 2 T 45 47.12 4 0d/s 2 6o 9et are he mass of geo A mA and mg and &e specti adius oS the qydation K and K6 afe -the A ofthe ea A and B despetive. moment of ine\a of geos Now A and B ass ven mA(kA) CKa) ate as 2 x o 06) (o 06) -3 5.76 11o m2 KA. 2. 5.76 x10 2 m2 TB -

the mass moment of inexta of the is given as (m)Ck)12 x15) Tnital anguas velocity of (wa) Tnitial anqulos veloaty of ai (w), 2.5 x o' 472= 26.18 dad/s. 2.5 is = 2.5 (wc), = Fral ango veloci f qeas 2-5メ10- 432 = nd A 17 81 vad/s wc)2.5 x47.12 4 2-5 initial Kine he enesH o! Now he the system is ven as 2 TB + (26 13)2 (26-13)3 Ti 5.7 5.76 XIO X 0-2 Xh 432 I8. 75 23 Now the fnal ineie enedy of-the sastem is qiven as 2. T2 TA 2. 5.76X1o(7. 81) T2 5.46X10 O.27 379.73 48 丁 T2

We have IO N-m given numbey of vevolution f qeor paincible ves the Now ene wok MOc TT T2 379 7348 18. 7523 + oad 36.10 Oc that So is veyofuons Yumbes of iven as 5.75 ey the ootahion of eas A Now 2-5 Gc So 25 2-5x(36-10)7od A 28al vo as G ven tenge ntal fosce 2 2. 2 -3 x 5.76Xlo X (26-13)* FAXO O8 x go 25 -3 5. 76 Xlo x ts is FA eoa Sotha targential forre 5.26 N Fa