# Circular orbit - period

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?

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
Homework Helper
Gold Member
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
Homework Helper
Gold Member
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.)