You need to design an industrial turntable that is 63.0 in diameter and has a ki

Question

You need to design an industrial turntable that is 63.0 in diameter and has a kinetic energy of 0.260 when turning at 43.0 .

part a:
What must be the moment of inertia of the turntable about the rotation axis?
part b:
If your workshop makes this turntable in the shape of a uniform solid disk, what must be its mass?

additional information:
i keep getting the wrong answer for part a. please show me the steps . the way im thinking is for part a since moment of inertia = m*r^2
and they give the Kinetic energy i use k = 1/2 mv^2 and solve for m but i have to convert the rpm to m/s so i used the v(t) = rpm*r formula i dont know why im wrong but im getting 0.013. please help !!

Explanation / Answer

Diameter d = 63 cm Radius r = d/ 2               = 31.5 cm               = 0.315 m Kinetic energy K = 0.260 J Angular speed = 43 rpm                           = 43 x2 rad / 60 s                           = 4.502 rad / s We know K = ( 1/ 2) I 2 From this moment of inertia I = 2K / 2                                              = 0.0256 kg m 2 (b). For solid disk I = ( 1/ 2) mr 2 From this mass m = 2I / r 2                             = 0.5169 kg

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