Circular motion (planetary orbit) question

[theneedtoknow]

Homework Statement

A turntable is spinning at 100 rpms. It has a mass of 2kg and a radius of 0.1 meters. 2 blocks of mass 0.5kg fall simultaneously on 2 opposite ends of a diagonal and manage to stick. What is the new angular velocity of the turntable after the blocks stick?

Homework Equations

Moment of inertia of a spinning disk is 0.25 M R^2

The Attempt at a Solution

Well I know Linear momentum of the ntire system is supposed ot be conserved
Initially its just the table spinning... Linear momentum is L = Iw where I is the moment of inertia and w is the angular velocity.

So Linitial = 0.25 x (2kg) x (0.1m) ^ 2 x winitial
and since it does 100 rpm we can multiply it by 2Pi rads / revolution and again by 1 min / 60 sec and i get 10Pi/3 rad/s
so my L initial is Pi/6

Now since L is conserved, when the 2 blocks fall, the new L should be the same as L initial
the New L will be a combination of the angular mometum of the turntable and of the 2 blocks

so L final = Iwfinal + the linear momentum of the 2 blocks
treating them as point particles of mass 0.5 kg , 0.1m away from the axis of rotation, their individual momentum can be obtained ith the formula L = r x p = r x mv... and v is just wr so it can be simplified to L = wmr^2.. and the w is constrained to be equal to the final w of the turntable

so Lfinal = Ix wfinal + 2mr^2 x wfinal = Pi / 6
(since one is at distance r and the other at -r, but they get squared so it doesn't matter)

From here, I can solve for wfinal and that should give me the angular velocity of the turntable at the end.

I kind of had a question but i think I might have worked it out while typing this up to ask it... but just in case...is this a correct way of approaching these kinds of questions? I've never done anything on angular momentum before and was wondering if this is correct?

BTW don't ask what this has to do with planetary motion c ause it doesn't LOL

 

[LowlyPion]

Your approach looks correct.

Since Angular Momentum is conserved then

I₁ω₁ = I₂ω₂

Where ω = 2πf

 

[thomate1]

Your approach to solving this problem is correct. You correctly used the conservation of angular momentum to determine the final angular velocity of the turntable after the blocks stick. The moment of inertia and the linear momentum of the blocks were also correctly calculated. This type of problem is a good way to practice using conservation laws in physics. Keep up the good work!