Work on a whirling mass (Kleppner 2nd ed 5-5)

[TimSon]

Homework Statement

Mass m whirls on a frictionless table, held to circular motion by a string which passes through a hole in the table. The string is pulled so that the radius of the circle changes from ri and rf.

a) show that the quantity L = mr^2(d(theta)/dt)
b) Show that the work in pulling the string equals the increase in kinetic energy of the mass

Homework Equations

F= ma where a is the acceleration in the radial direction
mg(ri - rh) = .5 * m * Vif^2 + .5*m*Vrf^2

The Attempt at a Solution

I first tried F = ma using the acceleration in terms of polar coordinates.

:x= second derivative of x
.x = second derivative of x
O = theta

-F = m(:r - r(.O)^2)
-F = m(r*.w - r(w)^2)

at this point i don't really know how to get from here since

 

[haruspex]

Start with part a). Show that the angular momentum is as per that formula.
When you have done that, you can find the linear speed at radius r, and from that find the tension as a function of radius.
(Take the pulling of the string to be very steady, so there is no radial acceleration beyond centripetal.)