Gradebook ORION Downiadable Testbook MESSAGE MY Chapter 11,Problem 041 The figur

Question

Gradebook ORION Downiadable Testbook MESSAGE MY Chapter 11,Problem 041 The figure shows a rigid structure consisting of a circular hoop of radus R and mass m, and a square made of four thin bars, each of length R and mass m. The rigid structure sotates at a constant speed about a vertical akis, with a period of rotation of 3.3 s IfR 1.8 m and m-3.6 kg clculate the angular momenturn about that axis. Units Click if you would like to Show Work for this question: taneurk Question Attempty: 0 of 10 used

Explanation / Answer

Moment of inertia of hoop,

I = 1/2*m*r2 + mr2 ( using parallel axis theorem)

I = 3/2*m*r2

I = 3/2*3.6*1.82

I = 17.496 kg.m2

Moment of inertia of square

for rod at distance R from axis , I = mR2

For two rod whose one end touches the axis,

I = 1/12mR2 + m(R/2)2

I = 1/3mR2

For rod along the axis, I = 0

Total inertia

Is = 2(1/3mR2) + mR2

Is = 5/3mR2

Is = 5/3*3.6*1.82

Is = 19.44 kg.m2

Itotal = 19.44 + 17.496

Itotal = 36.936 kg.m2

Angular velocity = 2*pi/T

w = 2*pi / 3.3 = 1.9039 rad/s

Angular momentum = Itotal * w

Angular momentum = 36.936 * 1.9039

Angular momentum = 70.322 kg m2 / s

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