Question

(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.

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=4m_er_e²+8m_hr_h² +(1/2)m_pr_p²

Part b.

As

m_e=210 kg , r_e=6.7m , m_h= 105 kg , r_h= 8.5 m , m_p= 1700 kg and r_p= 11 m

So

I=4$\times$210$\times$6.7² +8$\times$105$\times$8.5² +(1/2)$\times$1700$\times$11²=201247.6 kg m²

Par c.

Angular speed =2$\pi$/t

Part d.

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