A small disk and a bigger half disk

[billtodd]

Homework Statement

In the pic attached please look at the last figure below.
We have a half disk with moment of inertia $I_B$, and as the half disk completes a complete cycle of 180 degrees or $\pi$ if you prefer.
A small disk with mass $m$ which is smaller than the mass of the half disk, and velocity $v_0$, it's given that the mass of the small disk is much smaller than that of the half disk.
What will be the angular speed of the half disk

Relevant Equations

Torque here.

I believe the equation of torques is: $mgR\sin\theta- MR\dot{\theta}=I_B \ddot{\theta}$
And that of conservation of linear momentum is: $mv_0=I_B\dot{\theta}+mv_1$

I need to find $v_1$ and I know what are the initial conditions: $\theta(0)=\pi$ and $\dot{\theta}(0)=0$.

Then what is $v_1$ and how to find it?

Thanks!

 

[kuruman]

You have not described adequately what happens here. Is this a collision? If it is and if the collision is along the axis of symmetry of the half-disk (as appears to be the case), what reason does the half disk have to rotate clockwise as opposed to counterclockwise? The situation would be different if the collision were to take place off-axis. Do you see why and how?

 

[billtodd]

I think it should be $-\pi$, because the motion of the half big disk is counterclockwise.

 

[kuruman]

I think it should be $-\pi$, because the motion of the half big disk is counterclockwise.

What quantity should be $-\pi$? That's just a number without units. What reason do you have to say that the motion of the half disk is counterclockwise as opposed to clockwise? What criterion do you use to decide if it's one way or the other?

 

[billtodd]

@kuruman
It can't go up beyond the horizontal line because of gravity, its motion would be chaotic and not a simple harmonic. Or so I think.

 

[PeroK]

@kuruman
It can't go up beyond the horizontal line because of gravity, its motion would be chaotic and not a simple harmonic. Or so I think.

That's more a riddle than a problem statement!

 

[kuruman]

I still don't understand what the physical situation or the statement of the problem are. Can you translate the text that's in the figure? According to our rules, postings must be in English.

 

[billtodd]

I still don't understand what the physical situation or the statement of the problem are. Can you translate the text that's in the figure? According to our rules, postings must be in English.

I'll do the translation later on tomorrow. I got to regain my physics problem solving skills, they got really rusty.

It's not about that I don't remember the equations, I just never quite know how to choose the coordinate axes, etc.

 

[kuruman]

It's not about that I don't remember the equations, I just never quite know how to choose the coordinate axes, etc.

We are here to help you remember how to do it but we have to know the details of the task.

 

[haruspex]

Does the notation $I_B$ mean the half disk is hinged at B? If so, how is it moving at the start?