A ball of mass M and radius r1 on the end of a thin massless rod isrotated in a

Question

A ball of mass M and radius r1 on the end of a thin massless rod isrotated in a horizontal circle R0 about an axis of rotation AB.

a) Consider the mass of the ball to ber concentrated at its centerof mass, calculat its moment of inertia about AB

b) Using the parallel-axis theoren and considering the finiteradius of the ball calculate the moment of inertia about AB

c) Calculate the percentage difference introduced by th epoint massapproximation for r1=9.0cm and R0= 1.0m.



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Explanation / Answer

a) as mass is concentrated at the centerI=mRo2; b) as mass is not concentrated at the center the I about the diameterof the sphere is 2/5mr2 appling parallel axis theorem I about the axis is2/5mr2+mRo2. c) putting the values we have Ia=m*1*1=m;                                        Ib=2/5m*0.092+m*1*1=1.00324m percentage difference is (1.00324m-m)/m*100 =0.324percentage.

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