Angular Momentum/Impulse Problem

[cdbowman42]

1. A 1.8 kg, 20 cm diameter turntable rotates at 160 rpm on frictionless bearings. Two 500 g blocks fall from above, hit the turntable simultaneously at opposite ends of a diagonal, and stick. What is the turntable's angular velocity, in rpm, just after this event?


2. Angular momentum(L)=angular velocity(w)*moment of inertia(I)


3. I'm confused as to whether or not to appraoch this as a conservation of momentum problem or some other way. I think I would need to know the velocities of the blocks before they hit to to this.

 

[olivermsun]

Do the blocks carry with them any angular momentum of their own? (It seems the problem is set up to hint that they do not).

 

[cdbowman42]

Thanks! that's all I needed!

 

[tiny-tim]

hi cdbowman42!

I think I would need to know the velocities of the blocks before they hit to to this.

hint: what was their angular momentum about the axis, before they hit?

(assuming they fell vertically at speed v)

 

[AlexChandler]

I would think about it in the following way

$$\int \tau dt = \Delta ( I \omega)$$

where $$\int \tau dt$$ is the angular impulse and $$\Delta (I \omega)$$ is the change in angular momentum.

We can see that no vertical torque is exerted on the turntable, so the angular momentum must remain constant.

Then we must have

$$(I \omega)_{initial} = (I \omega)_{final}$$