Spinning puck rotational motion

[amohamed]

Homework Statement

A puck, mass m, on the end of a (thin, light) string rotates in a circle of radius r_0
at a speed v_0
on a
frictionless table. The radius of the circle is slowly reduced from its initial value by pulling the string
through a hole in the table.

A. Hence write down an expression for the speed of the mass when the radius is reduced to some radius
r
B. Write down an expression for the tension in the string and show it goes like 1/r^3

Homework Equations

v=rw

The Attempt at a Solution

i split the above problem into two systems. rotational and kinematic. the kinetic energy is
0.5mrw^2-0.5^mr_0w^2. For the rotational system i am unsure how this is linked to tension ?. Is my starting point correct ?.

 

[Spinnor]

What is the angular momentum of the system before the string is shortened?

What is the tension?

After the string is shortened does the angular momentum change?

If not, then you can figure the velocity as a function of the strings length and with that figure out the tension.

Good luck!