A disk h aving mass M and radius R spins about an axis through its center and pr

Question

A disk h

aving mass M and radius R spins about an axis through its center and prependicular to the flat face of the disk at angular velocity . A thin rod whose length is equal to the radius of the disk and whose mass is (3/2) M drops onto the diskand sticks to it as shown. (a) calculate the moment of inertia of the rod about one end.(b) calculate the final angular velocity of the composite object.(c) how much kinetic energy is lost in the collision? Recall I disk =(1/2) MR2and I rod,cm =(1/12)ML2

Explanation / Answer

a) Moment of inertia = Icm + (3/2M)(L/2)^2 = 1/3 (3/2)ML^2 = 1/2 ML^2

b) Moment of inertia of the composite object = 1/2ML^2 +1/2ML^2 =ML^2

final angular vel = x

ML^2(x) = 1/2ML^2 (v)

x = v/ 2 where v = initial angular vel

c) energy lost = 1/2(1/2ML^2) v^2 - 1/2 (ML^2) x^2 = 1/8ML^2v^2 half the initial energy

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