2: Rotational Impulse: Long after humans become extinct, alien explorers find a

Question

2: Rotational Impulse: Long after humans become extinct, alien explorers find a 12.0cm diameter DVD in a garbage can at the top of Mt Everest. They build a special player which floats the 16.0g DVD on a cushion of gas, and spin up from rest using the rotational impulse from part A. Unfortunately the ancient disk is very fragile so the broccoli shaped creatures examining it are only mildly shocked when the disk (now fully up to speed) explodes in a "poof" of shattered fragments thereby destroying the last memory of our race (and the dorsal eyestalk of the closest alien). What was the final angular velocity of the DVD, in Radian per see, before it went poof?

Explanation / Answer

Q2. let the magnitude of rotational impulse form the previour question be Q

then

moment of inertia of the disc = 0.5mr^2

m = 16*10^-3 kg

r = 12 *10^-2 m

hence

moment of inertia I = 0.5mr^2 = 0.0001152 kg m^2

so final angular speed be w

then

Q = Iw

w = Q/I = 8680.55Q rad/s where Q is in Ns

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