Prelat 3: In the following apparatus, the auxiliary platteris dropped onto the m

Question

Prelat 3: In the following apparatus, the auxiliary platteris dropped onto the main platter. Auxiliary Platter Main Platter Spindle The main platter has a rotational inertia IM and an initial angular velocity wo. The auxiliary platter has a rotational inertia lA and is initially not spinning. a.) Explain why the two platters will have the same final angular velocity. b) What implications does your answer to Part (a have for the conservation of angular momentum in this system? For the conservation ofrotational kinetic c.) Using conservation of angular momentum, find an expression for the final angular velocity of the system assuming the two platters have the same final angular velocity. d. Using your answer to Part (c above, show that the ratio offinal kinetic energy to initial kinetic energy is given by the expression below: KR IM Ko IM IA

Explanation / Answer

a)

Due to friction, the main platter will slow down and due to that exact friction, the uxillary platter will speed up..

Now, when both have same speed, the relative motion between the two platters will become 0. and thus thus the friction will be 0 and thus they will move with that same angular velocity .

b)

Angular momentum is conserved. but due to friction, the kinetic energy is not conserved.

c)

Initial angular momentum of the system : Im*Wo + Ia*0 = Im*Wo

Final angular momentum : Im*W + Ia*W = (Ia + Im)*W

Using the conservation of angular momentum :

(Ia + Im)*W = Im*Wo

So, W = Im*Wo/(Ia + Im) <----final angular velocity of the combination

d)

initial KE of the system : Ko = 0.5*Im*Wo^2 + 0.5*Ia*0^2 = 0.5*Im*Wo^2

Final KE : Kf = 0.5*(Im+Ia)*W^2 = 0.5*(Im +Ia)*( Im*Wo/(Ia + Im) )^2 = 0.5*Im^2*Wo^2/(Im+Ia)

So, ratio = Kf/Ko = 0.5*Im^2*Wo^2/(Im+Ia) / (0.5*Im*Wo^2) = Im/(Im+Ia) <---- PROVED

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