QuestionDetails: Consider a thin 46 m rodpivoted at one end. A uniform density s

Question

QuestionDetails: Consider a thin 46 m rodpivoted at one end. A uniform density spherical object (whose massis 2 kg and radius is 12 m) is attached to the free end of the rodand the moment of inertia of the rod about anend is Irod= 1 / 3 mL^2 and themoment of inertia of the sphere about its center of mass isIsphere = 2 / 5 mr^2 . QuestionDetails: Consider a thin 46 m rodpivoted at one end. A uniform density spherical object (whose massis 2 kg and radius is 12 m) is attached to the free end of the rodand the moment of inertia of the rod about anend is Irod= 1 / 3 mL^2 and themoment of inertia of the sphere about its center of mass isIsphere = 2 / 5 mr^2 . What is the angular acceleration of therod immediately after it is released from its initial position of63? from thevertical? The acceleration of gravity g = 9.8 m/s2 .Answer in units ofrad/s2.

Explanation / Answer

L = 46 m, m = 2 kg, r = 12 m, Irod = mL2/3, Isphere = 2mr2/5, = 63o, find the angularacceleration
torque = mg(L/2)*sin + mg*(L + r)sin =mg(3L/2 + r)sin
moment of inertia about the pivot I = Irod +[Isphere + m(L + r)2] = mL2/3 + 2mr2/5 + m(L +r)2
= /I = g(3L/2 +r)sin/[L2/3+ 2r2/5 + (L +r)2] = 0.171 rad/s2

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