Is Angular Momentum Conserved During the Changing of the String Length?

[AlexanderIV]

Homework Statement

An object with mass m is attached to a string with initial length R, and moves on a frictionless table in a circular orbit with center C as shown in the figure. The string is also attached to the center, but its length is adjustable during the motion. The object initially moves with velocity v and angular velocity ω.
Given: m = 500 g, v = π m/s, R = 50 cm
If the length of the string is shortened from R to r = R/2 while the mass is moving, what will be the new period in SI units?

Homework Equations

T = (2πR) / v

The Attempt at a Solution

T = (2πR) / v = (2π0.5) / π = 1
=> T = (2πR/2) / v = 0.5 s

But apparently 0.5 is not the correct answer and I do not understand why.

 

[TSny]

T = (2πR) / v = (2π0.5) / π = 1
=> T = (2πR/2) / v = 0.5 s

But apparently 0.5 is not the correct answer and I do not understand why.

Does the speed change when the string is shortened?

 

[AlexanderIV]

Does the speed change when the string is shortened?

No, it doesn't.

 

[TSny]

No, it doesn't.

Can you think of any physical quantity that remains conserved during the changing of the length of the string? (Maybe it's something you have recently covered in your course.)