A device consisting of four heavy balls connected by low-mass rods is free to ro

Question

A device consisting of four heavy balls connected by low-mass rods is free to rotate about an axle. It is initially not spinning. A small bullet traveling very fast buries itself in one of the balls. In the diagram, m = 0.005 kg, v = 400 m/s, M1 = 1.7 kg, M2 = 0.3 kg, R1 = 0.7 m, and R2 = 0.4 m. The axle of the device is at the origin < 0, 0, 0 >, and the bullet strikes at location < 0.216, 0.666, 0 > m.

Just after the impact, what is the angular speed of the device? Note that this is an inelastic collision; the system's temperature increases.

I tried

Angular momentum initial = Angular momentum final
mvr = Iw

and I solved for w


What am I doing wrong?

Explanation / Answer

please check if you have taken care of the following:

you need to consider the entire system while doing the angular momentum conservation

to find the velocity of the combined [ball + embeded bullet] you need to break down the velocity of bullet to components parallel to and perpendicular to the rod attaching M1-M1 and then for the tangential component apply momentum conservation to find the new tangential velocity of the embedded [bullet + ball] system and thereafter divide that tangential velocity of the combined [ball + bullet] by R1 to get .

while finding the changed angular momentum use the new moment of inertia taking care of the bullet +ball mass for M1 used initially for one of the 2 balls

Hope this helps

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