Academic Integrity: tutoring, explanations, and feedback — we don’t complete graded work or submit on a student’s behalf.

The figure below shows three 0.0130 kg particles that have been glued to a rod o

ID: 1497009 • Letter: T

Question

The figure below shows three 0.0130 kg particles that have been glued to a rod of length L = 5.40 cm and negligible mass. The assembly can rotate around a perpendicular axis through point O at the left end. (a) Assume one particle (that is, 33% of the mass) is removed. By what percentage does the rotational inertia of the assembly around the rotation axis decrease when that removed particle is the innermost one? % (b) What is the percentage decrease when that removed particle is the outermost one? %

Explanation / Answer

I = m [d^2 + (2d) ^2 + (3d) ^2] = 14 m d^2

When inner most is removed:
I1 = m {(2d) ^2 + (3d) ^2}

I –I1 = m d^2

[I –I1] /I = m d^2 / 14m d^2 = 1/14 = 7.143 %
======================================
When outer most is removed:
I –I1 = 9m d^2
[I –I1] /I =9 m d^2 / 14m d^2 = 9/14 = 64.29%