I need help understanding how to calculate the kinetic energy of the of the disk

Question

I need help understanding how to calculate the kinetic energy of the of the disk. I can't seem to get 25.5 J as my final answer. Show work please.

Problem 21.32 Part A The 5-kg circular disk spins about ABwith a constant angular velocity of w1-15 rad/s Simultaneousy, the shaft to which arm CAB is rigidly altached. rotates with constant angular velocity of 2 Determine the angular momentum of the disk about point Express your anawer in terms of the unit vectors i,j and k. To denote vectors in your anawers, be sure to select the vec' button. 6 ra/s. Fiue 1) Ho 0.3751+7.575k kg./s Submit My Answer Give Up Correct Part B Determine the kinetic energy of the disk Express your answer to three significant figures and include the appropriate units, T 25.5 J Submit My Answers Give Up Correct 2-6 rad/s Continue 0.3 04 m 15 rad/s 0,1 m

Explanation / Answer

=so, for part B, the total KE of the system has to be calculated in parts and then added
so, rotational KE of the spinning disc = 0.5Iw^2
I ( moment of inertia of the disc) = 0.5mr^2
m ( mass of disc) = 5kg
r ( radius ) of disc = 0.1 m
w ( angular velocity) = 15 rad/s
so, KE-disc = 0.5*(0.5*5*0.1^2)*15^2 = 2.8125 J

moment of inertia of the disc about z axis = 0.25mr^2
so, moment of inertai about the axis about which the disc is rotating about z' axis = 0.25mr^2 + m(0.3^2 + 0.4^2) = 1.2625 kg m^2
ke due to this rotation = 0.5*1.2625*6^2 = 22.725 J
Net KE = 22.725 + 2.8125 = 25.5 J

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