i have the physics\' review sheet for the final exam, i have got most of answers

Question

i have the physics' review sheet for the final exam,

i have got most of answers but two problems, 13, 14

most of them are about the torque or inertia, i think... (not sure)


well i tried, and i want to check my answers, so could anyone help me with those two problems?

if you dont have enough time to do all two problems,

you can just do a one problem. i will still very appreciate.


thank you!!




i took picture of the problems, since the problems contain diagrams.

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this is what my buddy got, but he and i are not 100% sure the answer is right...

13)

Find the final angular velocity ?f of the bullet and rod system:

Conservation of angular momentum equation:

(1) Lf = Li,

where Lf is final, Li is initial.

NOTE: I'll use plain L (no subscript) for the length of the rod.

Since the rod is initially at rest, we need only consider the Li for the bullet:

(2) Li = m * Vv X r,

where:

Vv = the velocity vector
r = the radius of the circle of rotation

Substituting:

(2') Li = (M / 9) * v * sin30 * (L / 2)

= M * v * L / 36


The final angular momentum of the combined bullet and rod about the CM:

(3) Lf = If * ?f,

where:

(4) If = sum of moments of bullet and rod

= (M / 9) * (L / 2)^2 + M * L^2 / 12 (from Source 1)

= M * L^2 / 9


Substituting (2') and (3) into (1):

(5) If * ?f = M * v * L / 36

and solving for ?f:

(6) ?f = (M * v * L / 36) / If

and substituting (4) for If:

= (M * v * L / 36) / (M * L^2 / 9)

= v / 4L, which is (b)

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my buddy got this answer, but he is not 100% sure its correct.

is it correct?

and number 14, he and i have no clue how to solve the problems...

so as you see on the picture, i pretty much guessed...

help me out please!!

Explanation / Answer

Ans(13)=V/4L Ans(14)1.41 s please rate as life saver and if you want solution, just put in comments and I will give you the links of solutions

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