(9%) Problem 6: A rotating system consists of four particles, each of mass M 0.8

Question

(9%) Problem 6: A rotating system consists of four particles, each of mass M 0.81 kg, fixed at distances from the rotation axis that are all integer multiples of the length L 0.21 m. 13% Part (a) Enter an expression in terms of the quantities defined in the problem, for the moment of inertia of the system when each particle is fixed at distance L from the rotation axis. Grade S ummary Deductions Potential 100% 7 8 9 Submissions L4 5 6 Attempts remaining per attempt) 1 2 3 detailed view give up! Feedback: deduction per feedback. Hints: deduction per hint. Hints remaining

Explanation / Answer

a and b

. m = 0.81 Kg L = 0.21m

when each particle is fixed at distance L the moment of inertai I is given by

I = 4 M L^2 = 4 X 0.81 Kg X 0.21m X 0.21m = 0.14 Kg-m^2

c and d

When 3 particles are at distance L , they each contribute ML^2 to Moment of Inertia. The fourth ball fixed at the axis does not contribute to I

I = 3 M L^2 = 3 X 0.81 Kg X 0.21 m X 0.21 m = 0.11 kg-m^2

e and f

The two balls fixed on axis do not contribute any value to I

The other two give rise to I given by

I = M X L^2 + M X (2L)^2 = 5ML^2

= 5 X 0.81Kg X 0.21 m X 0.21 m = 0.18 Kg-m^2

g and h

One fixed on axis has no contribution to I

The two at distance 2L and one at L contribute as follows

I = 2 X M (2L)^2 + ML^2 = 9ML^2

= 9 X 0.81 Kg X 0.21 m X 0.21m = 0.32 Kg-m^2

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