A uniform spherical shell of mass 8.00 k g with diameter 54.0 c m has four small

Question

A uniform spherical shell of mass 8.00kg with diameter 54.0cm has four small masses of mass 2.30kg attached to its outer surface and equally spaced around it. This combination is spinning about an axis running through the center of the sphere and two of the small masses (Figure 1) .

What friction torque is needed to reduce its angular speed from 70.0rpm to 47.0rpm in a time interval of 34.0s ?

A uniform spherical shell of mass 8.00kg with diameter 54.0cm has four small masses of mass 2.30kg attached to its outer surface and equally spaced around it. This combination is spinning about an axis running through the center of the sphere and two of the small masses (Figure 1). What friction torque is needed to reduce its angular speed from 70.0rpm to 47.0rpm in a time interval of 34.0s ?

Explanation / Answer

we know that I*alpha = r*Friction

here I = 2/3 mr^2 + 2Mr^2 where m = 8kg and M = 2.3 kg and r = .54m

= 2.904 kg m^2

now alpha = [(70-47)*2pi/60]/34 = .071 rads^-2

so frictional torque = r*F = 0.20621 kgm^2s^-2

and frictional force applied = F = 0.3819 N

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