Two children ( m = 31.0 kg each) stand opposite each other on the edge of a merr
ID: 1350252 • Letter: T
Question
Two children
(m = 31.0 kg
each) stand opposite each other on the edge of a merry-go-round. The merry-go-round, which has a mass of 1.70 102 kgand a radius of 1.2 m, is spinning at a constant rate of 0.42 rev/s. Treat the two children and the merry-go-round as a system.
(a) Calculate the angular momentum of the system, treating each child as a particle. (Give the magnitude.)
(b) Calculate the total kinetic energy of the system. (joules)
(c) Both children walk half the distance toward the center of the merry-go-round. Calculate the final angular speed of the system.
Explanation / Answer
a) Moment of inertia I = ((1/2)*M*R^2 + (m*R^2)
Inet = ((0.5 *170*1.2*1.2)+(31 * 1.2*1.2)
net Inertia = 167.04 kgm^2
Total angular momentun L = IW
L = 167.04 * 0.42
L = 70.15 Kgm/s
--------------------------------------------------
total KInetic energy = 0.5 IW^2
KE = 0.5 * 167.04 * 0.42*2pi* 0.42*2pi
KE = 581.63 Joules
----------------------------
as V = r W
W2/W1 = r1/r2
W2 = 0.42 * 2pi/0.5
W2 = 5.27 rad/s or 8.28 rev/s
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