A 33kg 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 78kg and a radius of 2.20m. Lindsey's linear velocity was 9 m/s at the moment she jumped onto the merry-go-round.

What is the initial angular momentum?

I am using the formula 1/2 mr^2 * w(initial).

Whatever I do is wrong, and I'm not sure if it is because I have the wrong formula or because I am not converting units properly..

Circumference = pi*2r = 3.14 * 4.4 = 13.8 m.

Va = 9m/s * 6.28rad/13.8m = 4.1 rad/s. = Angular velocity.

You have the wrong formula. The equation you're using for angular momentum calculates the moment of inertia for the merry-go-round (disk), not Lindsey. As the question states, "Hint: Although she started with linear velocity, consider the moment JUST BEFORE she landed on the merry-go-round." Therefore, we need to use an equation that calculates the moment of inertia for Lindsey. This would be: L= m(r^2)w. Since w=v/r, the final equation can be simplified to: L=mrv.

To find the initial angular momentum, you need to use the correct formula. The formula you mentioned, 1/2mr^2 * w, is actually the formula for rotational kinetic energy. The formula for angular momentum is different and is given by L = Iw, where L is the angular momentum, I is the moment of inertia, and w is the angular velocity.

To calculate the initial angular momentum, you first need to determine the initial angular velocity. The linear velocity (v) and angular velocity (w) are related through the equation v = rw, where r is the radius. Rearranging this equation, we have w = v/r.

Given that Lindsey's linear velocity (v) is 9 m/s and the radius (r) of the merry-go-round is 2.20 m, we can calculate the initial angular velocity (w) as follows:
w = v/r
w = 9 m/s / 2.20 m
w ≈ 4.091 rad/s

Now that we have the value for the initial angular velocity (w), we can proceed to calculate the initial angular momentum (L). However, before we do that, we need to determine the moment of inertia (I) of the merry-go-round. The moment of inertia depends on the distribution of mass around the rotation axis.

For a solid disc with uniform density like a merry-go-round, the moment of inertia (I) is given by I = (1/2)mr^2, where m is the mass of the object and r is the radius. The given mass of the merry-go-round is 78 kg and the radius is 2.20 m. Plugging these values into the formula, we can calculate the moment of inertia (I) as follows:
I = (1/2)mr^2
I = (1/2)(78 kg)(2.20 m)^2
I ≈ 194.04 kg*m^2

Finally, we can calculate the initial angular momentum (L) using the formula L = Iw:
L = Iw
L = (194.04 kg*m^2)(4.091 rad/s)
L ≈ 793.37 kg*m^2/s

Therefore, the initial angular momentum of the system is approximately 793.37 kg*m^2/s.

Momentum = M*Va = 33 * 4.1 = 135.2.