Question

A space pod circles a space station at the end of a long tether line.

(a) How will the linear speed of the pod compare with its original speed when the line has

been pulled in to half its length?

(b) How will the linear speed compare when the line is pulled in to one-tenth its original

length?

Answer 1

Let the initial velocity and length are respectively. Then Initial angular momentum will be

When the lie has been pull into a half its length then there won't be any external torque hence angular momentum will remain constant. Then

Given that hence

Hence linear velocity becomes twice of initial velocity.

(b)

When the lie has been pull into a one-tenth of its length then there won't be any external torque hence angular momentum will remain constant. Then

Given that hence

Hence linear velocity becomes ten times of initial velocity.