Question

Two children, each with a mass of 24.6 kg, are at fixed locations on a merry-go-round (a disk that spins about an axis perpendicular to the disk and through its center). One child is 0.78 m from the center of the merry-go-round, and the other is near the outer edge, 2.79 m from the center. With the merry-go-round rotating at a constant angular speed, the child near the edge is moving with translational speed of 11.0 m/s.

(a) What is the angular speed of each child?

? 0.78 m		=  _____ rad/s
? 2.79 m		=  _____ rad/s

(b) Through what angular distance does each child move in 5.0 s?

? 0.78 m		= _____ rad
? 2.79 m		=  _____ rad

(c) Through what distance in meters does each child move in 5.0 s?

d 0.78 m		=  _____ m
d 2.79 m		=  _____ m

(d) What is the centripetal force experienced by each child as he or she holds on?

Fc, 0.78 m		=  _____ N
Fc, 2.79 m		=  _____ N

Which child has a more difficult time holding on?

Inner Child or Outer Child

Answer 1

(a)since no external torque is working so angular momentum will be conserved and system will keep moving with same angular velocity.

for child standing at the edge

v=11 m/s(translational velocity)

r=2.79m

since w is not changing so

=3.94 rad/sec
this will be same for both the childs.

(B)

(c)distance moved by child standing at radius 0.78m

=15.366m

distance moved by second child standing at radius 2.79m

s=58.509m

(d)centripital force

child at 0.78m

F=297.87N

for child at 2.79m

F=1065.45N