Question

The two rotor blades of 31-in. radius rotate counterclockwise with a constant angular velocity w = 0 = 2.2 rad/sec about the shaft at O mounted in the sliding block. The acceleration of the block is 20 = 4.1 ft/sec. Determine the magnitude of the acceleration of the tip A of the blade when (a) 0 = 0, (b) 6 = 90°, and (c) 9 = 180º. Does the velocity of O or the sense of w enter into the calculation? 31" ao Answers: (a) aA = ft/sec (b) a A = ft/sec (c) 2A - ft/sec

Answer 1

Solution Given 8=31in = 2.58333ft a = o = 2.2 rad/ sec ao = 4.1 ft/sec² + Calculate the magnitude of the acceleration of the tip A of the blade when (a) @=0° =ão tanlo [-gn x-direction] 24.1tanlo o * At ou, then aalo coly. [sin (x) direction we get 0 - 41 - (2 2 2 58333 an = - 8. 403332 ft/sec a from ero, > And (b) When بي (2.27 x 2.58333 こ له 4 a Alo А AAlo = 12.50332 ft/sec 2 TT So QA = (4.1)? + (12.50332)! AA = 13.1584 ft /sed Ans

(C.) When 0=180° 22/12 Ho 77771 a Alo co} (in the x tve ac-disec dibertins (2.2²% x 2.58333 = = 12.50832ft/ see AAlo a A = 4.14 12.50332 = 16.60332 ft/sect AA = 16.60332 ft /sec2 Ang Answer (a) (as) at 0= 60 그 -8.403332 ft/sec2 (6) (AA) at o=90o = = 13.1584 ft/sec2 (c) (AA) at 0= 180° = 46.60332 ft/sec²