Angular velocity of a small object

[maevis18]

A small 0.870-kg object moves on a frictionless horizontal table in a circular path of radius 7.80 m. The angular speed is 9.85 rad/s. The object is attached to a string of negligible mass that passes through a small hole in the table at the center of the circle. Someone under the table begins to pull the string downward to make the circle smaller. If the string will tolerate a tension of no more than 1140 N, what is the radius of the smallest possible circle on which the object can move?



Can anyone help? i don't even know where to start. Help is greatly appreciated. :)

 

[tiny-tim]

Welcome to PF!

A small 0.870-kg object moves on a frictionless horizontal table in a circular path of radius 7.80 m. The angular speed is 9.85 rad/s. The object is attached to a string of negligible mass that passes through a small hole in the table at the center of the circle. Someone under the table begins to pull the string downward to make the circle smaller. If the string will tolerate a tension of no more than 1140 N, what is the radius of the smallest possible circle on which the object can move?

Hi maevis18! Welcome to PF!

Hint: The object will get faster and faster, just like an ice-skater turns faster when she pulls her arms in.

How fast can it go before the string breaks?

 

[maevis18]

thanks for that.

hmmm- I am assuming the angular momentum in both cases is the same.
I worked out the moment of inertia of the object at the bigger radius.
I = mr /2
(0.870)(7.8/2)
52.9308

angular momentum = (52.9308)(9.85)
= 521.37

any idea on where to go from here??

 

[tiny-tim]

thanks for that.

hmmm- I am assuming the angular momentum in both cases is the same.
I worked out the moment of inertia of the object at the bigger radius.
I = mr /2
(0.870)(7.8/2)
52.9308

angular momentum = (52.9308)(9.85)
= 521.37

any idea on where to go from here??

Yes … but you go first!