Harry Potter's Physics on a Rotating Turntable

[a.303]

Homework Statement

A turntable with I=400 kgm²/s and radius 2m is rotating at omega=2 rad/s. Harry Potter (HP) of mass 60 kg and Tri-Wizard Cup (TWC) of mass 20 kg are diametrically opposite to each other on the rim of the turntable.
a) What is HP's tangential velocity?
b) HP falls off tangentially. What is the omega, I and L of the turntable+TWC system?
c) HP jumps off radially from the rim. What is omega, I, L of the turntable+TWC system?
d) HP jumps off such that his tangential velocity is 2 m/s with respect to Earth. What is the omega, I and L of the turntable+TWC system?
e) HP jumps off such that his tangential velocity is 6 m/s with respect to Earth. What is the omega, I, and L of the turntable+TWC system?
f) HP jumps up high vertically. What is the omega, I and L of the turntable+TWC system?
g) HP starts walking along the rim of the turntable at 2 m/s w.r.t. Earth. What is the new omega of turntable+TWC system as he walks?
h) HP randomly walks toward the TWC and stops very close to it. What is the omega, I and L of the turntable+TWC+HP system?
i) HP touches the TWC which turns out to be a port-key. Both HP and TWC disappear. What is the new omega, I and L of the turntable? Assume zero torque.

Homework Equations

L=rpsin(theta)
L=I*omega
p=mv
I=cMR²

The Attempt at a Solution

a) v=2 rad/s*(4pi m/2pi rad)= 4 m/s
b)I initial= (m1+m2)4*c
I final= 400- .5*M*R²=340 kgm²/s

 

[haruspex]

b)I initial= (m1+m2)4*c

What is c? What about the I of the turntable?

I final= 400- .5*M*R2=340 kgm2/s

How can the MoI of the TWC system be less than that of the turntable alone?
What about the angular momentum (L) of the system after HP leaves?

 

[Rohan1997]

Tangental velocity is wr which is 4

 

[haruspex]

Tangental velocity is wr which is 4

a.303 already got that (and better, included units).