Question

6. Gear A rotates with an angular velocity of 0,= 20 rad/s, where 0, is the angular displacement of gear A, measured in radians. Gears A, B, C, and D have radii of 20 mm, 50 mm, 25 mm, and 100 mm, respectively. When , = 2 rad , Find: i) The angular velocity of gear A ii) The angular acceleration of gear A iii) The angular velocity of gear B iv) The angular acceleration of gear B v) The angular velocity of gear C vi) The angular acceleration of gear C vii) The angular velocity of gear D viii) The angular acceleration of gear D (30 points)

Answer 1

Greard Geart Giren that WA = 2 812 radls Gear Gear B DA is in rad Angular displacement A = z rad For relocity Radii of gears A = 20MM gears V, = ² Cr=rw) r₂ Wal MB = 50MM 9, w, re 25MM rD 100MM 9,9,=%2% (at), = Cath, s For gears, peripheral relocity of two years are equal → For gearu, tangential acclerations of tengutial accleration Cat=ra) two gears are equal WA = 20 A2 8A=2rad = 2(2)² Angular displacement WA 8 radlo

For B and a For AEB Because the gears NA WA = MB WB B and c are 508 WB on the same 20 x 8 = shayt WB = 3.2 radlo WB = Wc = 3.2radla We = 3.2 radla For c and D rc wc =rowo 25 * 3.2 = 100% WD WD=0.8 radls WA = 20A Differential on both sides dwa (20) dw dt = d dt dt do=W dt d (204) . DOA LA 11 dt doA 12 40A .doA dt LA= 4OA WA > 4x2x8 64 radla KA

For AGB For B&C MALA=0B LB are on 20 x64 = 50xdB Because the gears Bandc the same shaft dB=dc 25.6 radlo LB= 25.6 rad/a² dc = For C&D re&c=road 254 25-6 = 100 XRD L = 6.4 radle² relocity of gear (iii) The (v) The of gear B ;) The The angular relocity of gear A (WA)=sradla 1.) The angular accleration of gear A (LA) = 64 radla? angular B (WB) = 3.2 radla angular accleration B (20) = 25.6 medias (V) The angular relocity of gear c (We) = 3.2 radle (vin The argular accleration of gears (ac) = 25-6 rady? (vi) The angular relocity of gear (wo)= 0.8radle Gili) The angular accleration of gears (20) = 6.4 radla?