A 33.0 kg child named Lindsey runs as fast as she can and jumps onto the outer edge of a merry-go-round. The merry-go-round is initially at rest and has a mass of 78 kg and a radius of 2.20m . Lindsey's linear velocity was 9.0m/s at the moment she jumped onto the merry-go-round. What is the initial angular momentum of the system (in kgm^2/s )? [Hint: Although she started with linear velocity, consider the moment just before she landed on the merry-go-round.]
The initial angular momentum of the system can be calculated using the formula:
Angular momentum = moment of inertia x angular velocity
The moment of inertia (I) of the merry-go-round can be calculated using the formula:
Moment of inertia (I) = mass x radius^2
The mass of the merry-go-round is 78 kg and the radius is 2.20 m, so the moment of inertia (I) is:
I = 78 kg x (2.20 m)^2 = 350.16 kgm^2
The angular velocity (ω) of the merry-go-round can be calculated using the formula:
ω = v / r
Where v is the linear velocity (9.0 m/s) and r is the radius (2.20 m). So the angular velocity (ω) is:
ω = 9.0 m/s / 2.20 m = 4.09 rad/s
Now we can calculate the initial angular momentum (L) of the system:
L = I x ω
L = 350.16 kgm^2 x 4.09 rad/s
L ≈ 1430.9564 kgm^2/s
Therefore, the initial angular momentum of the system is approximately 1430.9564 kgm^2/s.