B) What is the moment of inertia of the two-disk system after they are rotating

Question

B) What is the moment of inertia of the two-disk system after they are rotating together?

C) What is the final angular velocity of the two-disk system? (Give both magnitude and direction using the given coordinate system.)

D) How much energy was lost to friction during this ?rotational collision??

E) If Disk #2 is given some initial angular velocity, the two disks can finish at rest (i.e. not rotating at all). What initial angular velocity is needed for this end result? (Give both magnitude and direction using the given coordinate system.)

Explanation / Answer

(a) Inertia of disk 1 = I1 = 1/2*0.7*0.142 = .00686 kg-m2

Inertia of disk 2 = I2 = 1/2*0.9*0.12 = 0.0045 kg-m2

(b) Inertia of combined disk = I1+2 = I1+I2 = 0.01136 kg-m2

(c) Initial angular momentum = J1 = I11 = 0.00686*4 = 0.0862 kg-m2/s

Final angular momentum = J2 = I1+21+2 = 0.01136*1+2

Angular momentum conservation implies, J1 = J2

So, 0.0862 = 0.01136*1+2

So, 1+2 = 7.58 rad/s. This will be the final angular speed of two-disk system.

(d) Initial rotational kinetic energy = 1/2*I112 = 1/2*0.00686*(4)2 = 0.541 J

Final KE = 1/2*I1+21+22 = 1/2*0.01136*7.582 = 0.326 J

Energy lost to friction = change in KE = 0.541-0.326 = 0.215 J

(e) Suppose initial velocity of disk 2 be 2.

Doing angular momentum conservation, 0.00686*4 + 0.0045*2 = 0.

this gives, 2 = -19.14 rad/s (Negative sign implies clockwise direction when viewed from top.)

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