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(7%) Problem 14: A merry-go-round at an amusement park consists of an outer ring of horses...

(7%)Problem 14:  A merry-go-round at an amusement park consists of an outer ring of horses and an inner ring of elephants. The ring of eight horses has a radius of rh = 8.5 m. Each of the eight horses has a mass mh = 105 kg. The ring of four elephants has a radius of re = 6.7 m and each of the four elephants has a mass me = 210 kg. The platform of the merry-go-round itself has a mass of mp = 1700 kg and a radius of rp = 11 m. At its operating speed, the merry-go-round makes one revolution every t = 11 s.
25% Part (a) Enter an expression for the total moment of inertia of the carousel about its axis, in terms of the defined quantities. I =|αβθdghmmemhmpPrerhrpt()789HOME↑^^↓456←/*123→+-0.END√()BACKSPACEDELCLEARGrade SummaryDeductions0%Potential100%SubmissionsAttempts remaining: 10 (10%per attempt)detailed viewHints:  5%  deduction per hint. Hints remaining:  2Feedback:  0%  deduction per feedback.25% Part (b) Calculate the moment of inertia of the carousel about its axis, in units of kilogram meters squared. 25% Part (c) Enter an expression for the angular speed of the carousel, in terms of the defined quantities. 25% Part (d) Calculate the carousel’s angular speed, in radians per second.


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Answer #1

Part a.

Total moment of inertia =Moment of inertia of elephants+Moment of inertia horses+Moment of inertia of merry go round

I=4mere2+8mhrh2 +(1/2)mprp2

Part b.

As

me=210 kg , re=6.7m , mh= 105 kg , rh= 8.5 m , mp= 1700 kg and rp= 11 m

So

I=4\times210\times6.72 +8\times105\times8.52 +(1/2)\times1700\times112=201247.6 kg m2

Par c.

Angular speed =2\pi/t

Part d.

Angular speed =2\pi/11=0.57 rad/sec

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