Find the moment of interia for the dumbbell pictured here assuming that the two

Question

Find the moment of interia for the dumbbell pictured here assuming that the two spheres are solid, that they have a radius of 10 cm for each one and that they are separated by the bar of 12. cm.

Find the kinetic energy that this system if it is rotating at the rate of 10 revolutions per minute about the center of mass of the whole system as show.

Find the moment of interia for the dumbbell pictured here assuming that the two spheres are solid, that they have a radius of 10 cm for each one and that they are separated by the bar of 12. cm. Find the kinetic energy that this system if it is rotating at the rate of 10 revolutions per minute about the center of mass of the whole system as show.

Explanation / Answer

1.

If R is the radius of the dumbell & a is the length of the rod, M be the mass of dumbell, m be the mass of rod

I = 2 * [(2/5 M R^2) + ma^2]

I = 2*[2/5 * 70 * 10^2 + 5 * 12^2]

I = 2*[2800 + 720]

I = 7040

2.

Kinetic energy = 1/2 I * w^2

K.E = 1/2 * 7040 * 10^2

K.E. = 352000 J

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