Problem 10.58 9 of 15 > Considering the mass of the ball to be concentrated at i

Question

Problem 10.58 9 of 15 > Considering the mass of the ball to be concentrated at its center of mass, calculate its moment of inertia about AB Constants | Periodic Table Express your answer in terms of the given quantities A ball of mass M and radius r1 on the end of a thin massless rod is rotated in a horizontal circle of radius Ro about an axis of rotation AB, as shown in the figure (Figure 1). Submit Request Answer Part B Using the parallel-axis theorem and considering the finite radius of the ball, calculate the moment of inertia of the ball about AB Express your answer in terms of the given quantities. Submit Request Answer Part C Figure 1 of 1 Calculate the percentage error introduced by the point mass approximation for r1 8.0 cm and Ro- 1.2 m Express your answer using two significant figures 0 Error- Submit Request Answer

Explanation / Answer

PART A:

if we assume the whole mass concentrated at center then it can be treated as a point mass

moment of inertia about AB = MRo2

PART B:

moment of inertia abount an axis passing through center and parallel to AB =Io = (2/5)Mr12

moment of inertia about axis AB = Io + Ml2

I = MRo2 +(2/5)Mr12

PART C :

I for a point mass = M(1.2)2 = 1.44M

I for a sphere = 1.44M +(2/5)M(0.08)2

I = 1.44256M

percentage error = (0.00256M/1.44256M)*100 = 0.178 %

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