I am pretty sure I figured out 19 to be e.3/5 and now I am stuck on how to figur

Question

I am pretty sure I figured out 19 to be e.3/5 and now I am stuck on how to figure out 20.

19. A disk of mass M and radius R is rotating with an angular velocity . A rod also of mass M but length 2R is initially not rotating. It is dropped vertically onto the rotating disk as shown in the figure. After the collision, the disk and rod rotate together with an angular velocity of

a) b) 6/7 c) 3/4 d) 2/3 e) 3/5 f) none of the above

20. What fraction of the initial kinetic energy was lost in the collision in question 19? Choose the closest.
a) 0 b) 0.2 c) 0.4 d) 0.6 e) 0.8

Explanation / Answer

Applying angular momentum conservation,

Ii wi = If wf

(M R^2 / 2) (w) = ((MR^2 /2) + (M (2R)^2 / 12))wf

w/2 = (1/2 + 1/3) wf

w/2 = 5 wf/6

wf = 3 w / 5

Ans(e)

20. Ki = (M R^2 / 2) (w^2) /2 = M R^2 w^2 / 4

Kf = (5 M R^2 /6) (3w/5)^2 / 2 = 3 M R^2 w^2 / 20

Klost = Ki - Kf = M R^2 w^2 / 10

fraction = (1/10) / (1/4) = 0.4

Ans(C)

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