Question

Three children are riding on the edge of a merry-go-round that is 105 kg, has a...

Three children are riding on the edge of a merry-go-round that is 105 kg, has a 1.70-m radius, and is spinning at 24.0 rpm. The children have masses of 22.0, 28.0, and 33.0 kg. If the child who has a mass of 28.0 kg moves to the center of the merry-go-round, what is the new angular velocity in rpm? Ignore friction, and assume that the merry-go-round can be treated as a solid disk and the children as points.

Homework Answers

Answer #1

Moment of inerta of the merry-go-round = 1/2 Mr2, M = 105 kg, r = 1.7 m
Moment of inertia of all the three children = m1r2 + m2r2 + m3r2
m1 = 22 kg, m2 = 28 kg, m3 = 33 kg
Total initial moment of inetia, Ii = [M/2 + m1 + m2 + m3] r2
= [105/2 + 22 + 28 + 33] x (1.7)2
= 391.595 kg m2.
Initial angular velocity, i = 24 rpm

Final moment of inertia
When the child with mass 28 kg is movend to the center, he is not contributing to the net moment of inertia since r = 0 at the center.
If = = [105/2 + 22 + 33] x (1.7)2
= 310.675 kg m2.
Take f is the final angular momentum.

Since there is no external torque, angular momentum is conserved.
Ii x i = If x f
f = [Ii x i] / If
= [391.595 x 24] / 310.675
30.25 rpm

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Three children are riding on the edge of a merry-go-round that is 105 kg, has a...
Three children are riding on the edge of a merry-go-round that is 105 kg, has a 1.60-m radius, and is spinning at 22.0 rpm. The children have masses of 22.0, 28.0, and 33.0 kg. If the child who has a mass of 28.0 kg moves to the center of the merry-go-round, what is the new angular velocity in rpm? Ignore friction, and assume that the merry-go-round can be treated as a solid disk and the children as points.
Three children are riding on the edge of a merry-go-round that is 142 kg, has a...
Three children are riding on the edge of a merry-go-round that is 142 kg, has a 1.60 m radius, and is spinning at 17.3 rpm. The children have masses of 22.4, 29.0, and 38.8 kg. If the child who has a mass of 38.8 kg moves to the center of the merry-go-round, what is the new angular velocity in rpm?
Three children are riding on the edge of a merry-go-round that is 142 kg, has a...
Three children are riding on the edge of a merry-go-round that is 142 kg, has a 1.60 m radius, and is spinning at 19.3 rpm. The children have masses of 22.4, 30.5, and 34.8 kg. If the child who has a mass of 34.8 kg moves to the center of the merry-go-round, what is the new angular velocity in rpm?
Three children are riding on the edge of a merry-go-round that is a solid disk with...
Three children are riding on the edge of a merry-go-round that is a solid disk with a mass of 95.8 kg and a radius of 1.72 m. The merry-go-round is initially spinning at 5.84 revolutions/minute. The children have masses of 29.0 kg, 28.2 kg and 33.6 kg. If the child who has a mass of 28.2 kg moves to the center of the merry-go-round, what is the new angular velocity in revolutions/minute?
Three children are riding on the edge of a merry-go-round that is a disk of mass...
Three children are riding on the edge of a merry-go-round that is a disk of mass 92 kg, radius 1.4 m, and is spinning at 23 rpm. The children have masses of 24 kg, 28.4 kg, and 34.2 kg. Randomized VariablesM = 92 kg m1 = 24 kg m2 = 28.4 kg m3 = 34.2 kg r = 1.4 m f = 23 rpm    If the child who has a mass of 28.4 kg moves to the center of the...
A 36.5 kg child stands at the center of a 125 kg playground merry-go-round which rotates...
A 36.5 kg child stands at the center of a 125 kg playground merry-go-round which rotates at 3.10 rad/s. If the child moves to the edge of the merry-go-round, what is the new angular velocity of the system? Model the merry-go-round as a solid disk.
Two children, Angelica (mass 25 kg) and Boris (mass 50 kg), are playing on a merry-go-round...
Two children, Angelica (mass 25 kg) and Boris (mass 50 kg), are playing on a merry-go-round (which you can assume is a solid disk with mass 225 kg and radius 1.5m). Assume that any friction on the axle of the merry-go-round is negligible. Part A: Angelica starts spinning the merry-go-round, giving it an angular velocity of 8 rad/s, then she stops pushing it. Boris runs with a speed of 6 m/s directly toward the center of the merry-go-round. He jumps...
a 40 kg child is standing on the edge of a 100 kg merry go round(...
a 40 kg child is standing on the edge of a 100 kg merry go round( flat disk), with a radius of 4m. The merry go round is initially traveling at 20 rads/s. The child walks towards the center of the merry go round , until she is 0.5m from the center. What is the final angular speed other child at the new location?
A child with a mass of 50 kg is standing at the edge of a merry-go-round...
A child with a mass of 50 kg is standing at the edge of a merry-go-round which has a radius of 3.50 m and a mass of 700 kg. The merry-go-around is initially at rest. The child throws a 1.20 kg stone perpendicular to the merry-go-round's radius at a speed of 6.0 m/s. What is the resulting angular speed of the entire system? Friction is negligible and the merry-go-round is a uniform disk. The child is classified as a point...
Ben and Jerry are standing at the center of a 134 kg merry-go-round of radius 1.30...
Ben and Jerry are standing at the center of a 134 kg merry-go-round of radius 1.30 m that is already spinning at 3.00 rad/s. They proceed to walk in opposite directions toward the edge of the merry-go-round. If Ben reaches the edge while Jerry is halfway between the center and the edge, what will be the new angular velocity (in rad/s) of the merry-go-round? Assume Ben and Jerry can be modeled as point masses of 32.0 kg and 21.0 kg,...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT