Find mass of uniform solid disk?

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SUMMARY

The discussion centers on calculating the mass of a uniform solid disk designed as an industrial turntable with a diameter of 48.0 cm and a kinetic energy of 0.300 J at 31.0 rpm. The moment of inertia (I) for the turntable is established as 5.71×10^-2 kg m². The correct formula to determine the mass (m) is derived from I = 1/2 mr², leading to the conclusion that mass can be calculated using the relationship m = 2I/r², where r is the radius of the disk.

PREREQUISITES
  • Understanding of rotational dynamics
  • Familiarity with the moment of inertia concepts
  • Knowledge of kinetic energy in rotational motion
  • Ability to manipulate algebraic equations
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  • Study the derivation of the moment of inertia for various shapes, particularly solid disks
  • Learn about the relationship between kinetic energy and rotational motion
  • Explore practical applications of turntables in industrial settings
  • Investigate the effects of varying diameters on the mass and inertia of rotating objects
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Mechanical engineers, physics students, and professionals involved in the design of rotating machinery or industrial equipment.

saturn67
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you need to design an industrial turntable that is 48.0 cm in diameter and has a kinetic energy of 0.300 J when turning at 31.0 rpm

i found that inertia of the turntable about the rotation axis
is = 5.71×10^-2 kg m^2

If your workshop makes this turntable in the shape of a uniform solid disk, what must be its mass?

it try to use I=mr^2
so mass = I/r^2

but that don't work
 
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Woot it work thank you
 

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