Question

A 220 kg merry-go-round that is 2.1 meters in radius is rotating with a 24 kg girl standing 1 meter from the center. It is rotating with a period of 3.2 seconds.

1. What is the angular velocity of the merry-go-round?

2. What is the total moment of inertia of the merry-go-round and girl?

3. What is the total angular momentum of the merry-go-round and girl?

A 220 kg merry-go-round that is 2.1 meters in radius is rotating with a 24 kg girl. She moves to the outer edge of the merry-go-round.

4. What is the total angular momentum of the merry-go-round and girl after she's moved?

5. What is the moment of inertia of the merry-go-round and girl after she's moved?

6. What is the angular velocity of the merry-go-round and girl after she's moved?

7. What is the period of the merry-go-round and girl after she's moved?

8. How does this period compare to the start? Why is it different?

9. What is the linear velocity of the girl when she is on the edge of the merry-go-round?

The 24 kg girl accidentally lets go and is thrown off the merry-go-round.

10. How much linear momentum does she have right before she lets go?

Can you answer 1-10?

Answer 1

a)

w = 2pi /T = 2* 3.14 /3.2 = 1.9625 rad/s

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b)

I = I + mr^2 = 0.5* 220* 2.1^2 + 24* 1^2

I = 509.1 kg m^2

c)

L = ( I + mr^2) w = ( 0.5* 220* 2.1^2 + 24* 1^2)* 1.9625

L = 999.11 kgm^2/s

d)

angular momentum remains constant

L = 999.11 kg m^2

e)

I = 0.5* 220* 2.1^2 + 24* 2.1^2 = 590. 94 kg m^2

f)

w' = 999.11 / 590.94 = 1.691 rad/s

g)

T = 2 pi / w' = 3.714 s

h)

time increases due to increase in moment of inertia of system

i)

v = 2.1* 1.691 = 3.551 m/s

j)

P = mv = 24* 3.551 = 85.226 Kg m/s

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