child is at the center of a merry-go-round. The merry-go-round can be assumed to be a disk of mass M and radius R. The child can be considered to be a point mass one-quarter the mass of the merry-go-round (m=M/4). Initially the merry-go-round is rotating with angular velocity Wo about a vertical frictionless axis.(Wo is initial angular velocity)
d) Assume that instead of stepping off the merry-go-round the child turns 900 when he gets to the edge and starts walking tangentially around the rim. As a result the merry-go-round changes speed to 0.8Wo from the value 2Wo/3. Determine the speed of the child relative to the ground, and also his speed relative to the merry-go-round. Is the child walking in the direction of the rotation of the merry-go-round or in the opposite direction?
I was able to figure out that from 0.666Wo to 0.8Wo, the merry-go-round's increase in angular velocity can only mean that the child is moving opposite to the merry go round.
The part that I'm stuck on is the part where I use angular momentum conservation to find the child's speed relative to the ground.
You Don't have to solve the problem, just give me a general hint or guide for this problem, and I will be very thankful.
d) Assume that instead of stepping off the merry-go-round the child turns 900 when he gets to the edge and starts walking tangentially around the rim. As a result the merry-go-round changes speed to 0.8Wo from the value 2Wo/3. Determine the speed of the child relative to the ground, and also his speed relative to the merry-go-round. Is the child walking in the direction of the rotation of the merry-go-round or in the opposite direction?
I was able to figure out that from 0.666Wo to 0.8Wo, the merry-go-round's increase in angular velocity can only mean that the child is moving opposite to the merry go round.
The part that I'm stuck on is the part where I use angular momentum conservation to find the child's speed relative to the ground.
You Don't have to solve the problem, just give me a general hint or guide for this problem, and I will be very thankful.
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Where was the child when the speed was Wo ?
The (2/3)Wo seems to mean the child had already slowed down the merry go round by stepping onto the merry go round. (Maybe that was part a,b,c?)
Anyway, if the child is at the edge when the speed is (2/3) Wo,
then the angular momentum is
[(1/2)M+(1/4)M]R^2 (2/3)(Wo) = (1/2)MR^2 Wo
This will be conserved when the child starts walking around the edge of the merry go round.
So we have
(1/2)MR^2 Wo = (1/2)MR^2 (4/5)Wo + (1/4)MR^2 Wc
Dividing out MR^2 we have
(1/2)Wo - (2/5)Wo = (1/4)MR^2 Wc
Wc = (2/5)Wo. Relative to the ground, the child's speed is (2/5) Wo, but relative to the merry go round, it is -(2/5)Wo. Yes, he is walking in the direction opposite to the merry go round's motion.
The (2/3)Wo seems to mean the child had already slowed down the merry go round by stepping onto the merry go round. (Maybe that was part a,b,c?)
Anyway, if the child is at the edge when the speed is (2/3) Wo,
then the angular momentum is
[(1/2)M+(1/4)M]R^2 (2/3)(Wo) = (1/2)MR^2 Wo
This will be conserved when the child starts walking around the edge of the merry go round.
So we have
(1/2)MR^2 Wo = (1/2)MR^2 (4/5)Wo + (1/4)MR^2 Wc
Dividing out MR^2 we have
(1/2)Wo - (2/5)Wo = (1/4)MR^2 Wc
Wc = (2/5)Wo. Relative to the ground, the child's speed is (2/5) Wo, but relative to the merry go round, it is -(2/5)Wo. Yes, he is walking in the direction opposite to the merry go round's motion.