Density is a chemichal change
I would believe the opposite of malleable to be rigid, or stiff. :)
When its still the form of jelly, it is flammable, but it does not go everywhere or it doesn't evaporate.
Answer:
The final angular velocity is ![w_f = \frac{MR^2}{MR^2+ mr^2} w](https://tex.z-dn.net/?f=w_f%20%3D%20%5Cfrac%7BMR%5E2%7D%7BMR%5E2%2B%20mr%5E2%7D%20w)
Explanation:
From the question we are told that
The mass of the first disk is m
The radius of the first disk is r
The mass of second disk is M
The radius of second disk is R
The speed of rotation is w
The moment of inertia of second disk is ![I = \frac{1}{2} MR^2](https://tex.z-dn.net/?f=I%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20MR%5E2)
Since the first disk is at rest initially
The initial angular momentum would be due to the second disk and this is mathematically represented as
![L_i = Iw = \frac{1}{2} MR^2 w](https://tex.z-dn.net/?f=L_i%20%3D%20Iw%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20MR%5E2%20w)
Now when the first disk is then dropped the angular momentum of the whole system now becomes
![L_f = (I_1 + I_2 ) w_f= ( \frac{1}{2} MR^2 + \frac{1}{2} m^2 r^2) w_f](https://tex.z-dn.net/?f=L_f%20%3D%20%28I_1%20%2B%20I_2%20%29%20w_f%3D%20%28%20%5Cfrac%7B1%7D%7B2%7D%20MR%5E2%20%2B%20%5Cfrac%7B1%7D%7B2%7D%20m%5E2%20r%5E2%29%20w_f)
This above is because the formula for moment of inertia is the same for every disk
According to the law conservation of angular momentum
![L_f = L_i](https://tex.z-dn.net/?f=L_f%20%3D%20L_i)
![( \frac{1}{2} MR^2 + \frac{1}{2} m^2 r^2) w_f = \frac{1}{2} MR^2 w](https://tex.z-dn.net/?f=%28%20%5Cfrac%7B1%7D%7B2%7D%20MR%5E2%20%2B%20%5Cfrac%7B1%7D%7B2%7D%20m%5E2%20r%5E2%29%20w_f%20%20%20%20%3D%20%20%5Cfrac%7B1%7D%7B2%7D%20MR%5E2%20w)
=> ![w_f = \frac{\frac{1}{2} MR^2 w }{( \frac{1}{2} MR^2 + \frac{1}{2} m^2 r^2)}](https://tex.z-dn.net/?f=w_f%20%20%20%20%3D%20%20%20%5Cfrac%7B%5Cfrac%7B1%7D%7B2%7D%20MR%5E2%20w%20%7D%7B%28%20%5Cfrac%7B1%7D%7B2%7D%20MR%5E2%20%2B%20%5Cfrac%7B1%7D%7B2%7D%20m%5E2%20r%5E2%29%7D)
![w_f = \frac{MR^2}{MR^2+ mr^2} w](https://tex.z-dn.net/?f=w_f%20%3D%20%5Cfrac%7BMR%5E2%7D%7BMR%5E2%2B%20mr%5E2%7D%20w)