Question

For a short time, gear A of the automobile starter (Figure 1) rotates with an angular acceleration of aA = (5001/2) rad/s?, where o is in rad/s. Determine the angular velocity of gear B after gear A has rotated 50 rev, starting from rest. The radii of gears A and B are 10 and 25 mm respectively. [4 marks) Figure 1 1 B

Answer 1

Angular velocity of gear B is 328.904 rad/s

A = 208. 33 +3 SOLUTION Giuer angular acceleration of gear A, QA = 50w we know, dw dt => 50 W'2 dw at .. dt حیلے -- I 50 Integrating on both sides + idt = the whole O 112 -) t 50 % W = (25+)? w: 625 +2 but do dt de = 625+ 2 do 625+27 Again integrating on both sides 645+'de o Sdo - - 625 +3 625 here will be in radians 271 1 yev 100 TT 50 yev .. 100 T = 208.33 43 Solving for 't we get + = 1.147 Seconds

:: Angular velocity of geas A, CA = 625 +2 = 625 (1.147)2 rad/s 6 WA : 822.26 ras we know WARA COBOB =>(822.26) (10) = WA* 25 WB 328.904 rad/s) Anisu SWER