Problem 4: 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 = 8.5m. Each of the eight horses has a mass mh = 105 kg. The ring of four elephants has a radius of re = 6.6 m and each of the four elephants has a mass me = 190 kg. The platform of the merry-go-round itself has a mass of mp = 1650 kg and a radius of rp = 10.2 m. At it’s operating speed, the merry-go-round makes one revolution every t = 11s. Part (a) Enter an expression for the total moment of inertia of the carousel about its axis, in terms of the defined quantities.Expression :I = Select from the variables below to write your expression. Note that all variables may not be required.α, β, θ, d, g, h, m, me, mh, mp, P, re, rh, rp, tPart (b) Calculate the moment of inertia of the carousel about its axis, in units of kilogram meters squared.Numeric : A numeric value is expected and not an expression.I = Part (c) Enter an expression for the angular speed of the carousel, in terms of the defined quantities.Expression :ω = Select from the variables below to write your expression. Note that all variables may not be required.α, β, π, θ, d, g, h, m, me, mh, mp, P, re, rh, tPart (d) Calculate the carousel’s angular speed, in radians per second.Numeric : A numeric value is expected and not an expression.ω =

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter11: Gravity, Planetary Orbits, And The Hydrogen Atom

Section: Chapter Questions

Problem 51P

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Problem 4: 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 r_h = 8.5m. Each of the eight horses has a mass m_h = 105 kg. The ring of four elephants has a radius of r_e = 6.6 m and each of the four elephants has a mass m_e = 190 kg. The platform of the merry-go-round itself has a mass of m_p = 1650 kg and a radius of r_p = 10.2 m. At it’s operating speed, the merry-go-round makes one revolution every t = 11s.

Part (a) Enter an expression for the total moment of inertia of the carousel about its axis, in terms of the defined quantities.
Expression   :
I = __________________________________________

Select from the variables below to write your expression. Note that all variables may not be required.
α, β, θ, d, g, h, m, m_e, m_h, m_p, P, r_e, r_h, r_p, t

Part (b) Calculate the moment of inertia of the carousel about its axis, in units of kilogram meters squared.
Numeric   : A numeric value is expected and not an expression.
I = __________________________________________

Part (c) Enter an expression for the angular speed of the carousel, in terms of the defined quantities.
Expression   :
ω = __________________________________________

Select from the variables below to write your expression. Note that all variables may not be required.
α, β, π, θ, d, g, h, m, m_e, m_h, m_p, P, r_e, r_h, t

Part (d) Calculate the carousel’s angular speed, in radians per second.
Numeric   : A numeric value is expected and not an expression.
ω = __________________________________________

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