Calculating Angular Velocity: Puck in Circular Motion

[zoner7]

Homework Statement

A puck with mass 0.28 kg moves in a circle at the end of a string on a frictionless table, with radius 0.75 m. The string goes through a hole in the table, and you hold the other end of the string. The puck is rotating at an angular velocity of 18 rad/s when you pull the string to reduce the radius of the puck's travel to 0.55 m. Consider the puck to be a point mass. What is the new angular velocity of the puck?

The Attempt at a Solution

So we clearly have a centripetal force here caused by the pull of the string.
ooo... definitely just realized that I was given the mass. I was going to ask how in the world is the problem solvable without it. let me work some more and see what I come up with.

So, I believe that the centripetal acceleration is linear not angular. I need to somehow relate this linear acceleration to the change angular velocity and radius...

By the way, is it necessary to consider moment of inertia, or does it not matter because the object is already in motion? But since the object is accelerating...

Are there any good websites that explain moment of inertia nicely? I still do not completely understand it.

 

[zoner7]

So I browsed through my physics book and stumbled upon the concept of conservation of angular momentum.

Li = Lf
Iiωi = Ifωf

Although I have no idea what the moment of inertia of a puck is, i concluded that it is irrelevant because everything except the radii and the angular velocities cancel once you compare the two equations.

So I said that
Ri^2 * wi = Rf^2 * wf

Plugging in my values I got
0.75^2 * 18 = 0.55^2 * wf
Solving for wf I got 33.47 rad/s.

seems a little big to me. And, more importantly, I never even used the mass, which was given to me. Can anyone spot my error?

 

[naresh]

Just because the mass is given, it doesn't mean you have to use it

The moment of inertia of the puck does not matter because the problem asks you to treat it as a point mass.

Your solution looks fine to me.

 

[zoner7]

thank you :)
Trying to trick me with that given mass...
those problem designers are a little evil

 

[jimgram]

I believe you must use inertia. In the simplest form - that of a point mass, I=ms*r^2.
Your problem is that when r changes, so does I (as a squared function), so L also changes. To conserve L, w changes according to w=L/I

 

[naresh]

(Sorry, I meant the moment of inertia of the puck about its own axis in my prev post)