Consider the experiment and data below where a large massive disk is dropped ont

Question

Consider the experiment and data below where a large massive disk is dropped onto a rotating thin disk of smaller mass. Both disks have the same radii. Before doing this problem, predict whether or not the rotational kinetic energy is conserved. That is, does the initial rotational kinetic energy of the system rotational kinetic energy equal the final of the system? Your answer here will not affect your score. The question is only posed to give you the opportunity to think before you calculate. Using conservations of angular momentum, calculate omega y. Calculate the initial rotational kinetic energy of the system. Calculate the final rotational kinetic energy of the system. Calculate the percent change in energy and state whether or not kinetic energy is conserved. If the kinetic energy is not conserved, where did it go?

Explanation / Answer

1) No,rotational kinetic energy is not conserved

2) Using law of conservation of angular momentum

Initial angular momentum = Final angular momentum

Li = Lf

(I1*w1)+(I2*w2) = (I3*wf)

I is the moment of inertia of the disk = 0.5*M*R^2

(0.5*1.5*0.05^2*0)+(0.5*0.1*0.05^2*35) = (0.5*(1.5+0.1)*0.05^2*wf)

wf = 2.1875 rad/sec

3) initial rotational kinetic energy is Ki = 0.5*I*w^2 =0.5*0.1*0.05^2*35^2 = 0.153 J

4) Final rotational kinetic energy is Kf = 0.5*I*wf^2 = 0.5*(1.5+0.1)*0.05^2*2.1875^2 = 9.57*10^-3 J

5) percent change is delta k /Ki = ((9.57*10^-3)-(0.153))/0.153 = -0.937 = -93.7 %

negative sign showa that Kinetic energy is decreased

kinetic energy is not onserved

6) this change in kinetic energy is appered as the internal energy of the system

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