A merry-go-round can be modeled as a solid disk of radius R = 2m and mass M = 20

Question

A merry-go-round can be modeled as a solid disk of radius R = 2m and mass M = 200kg. Two persons, of masses m_1 = 70kg and m_2 = 80kg, are seated on the surface of the disk at distances r_1 = 1.6m and r_2 = 1.2m from the axis of rotation. (a) If we approximate the two persons as point-like, what is the moment of inertia of the system? (b) If the merry-go-round is spun by an electric motor providing a constant torque tau = 60Nm, how long does it take to reach an angular velocity omega = 20rev/min? (c) Calculate the centripetal acceleration of person 1 at 20rev/min.

Explanation / Answer

a) moment of inertia I = IDISC + Ipersons

   = 0.5*200*2^2 + 80*1.2*1.2 +70*1.6*1.6

   =694.4 kgm^2

b) Torque = i alpha

alpha = torque/i =60/694.4 = 0.0864 /s^2

w = 20 rev/min = 20*2pi/60 = 2.0944 /s

t = w/alpha = 2.0944/ 0.0864 = 24.24 seconds

c) a = w^2r

= 2.0944^2*1.6 = 7.02 m/s^2

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