Rotation problem - AP Physics 1

[blueblast]

Hey guys,

I'm having trouble understanding this problem that was on an AP Physics 1 sample questions page:

So a couple of questions here:
(By the way, I know the answer is C)

1. My teacher explained that the net torque here on the assembly would be zero(will ask him again later). Is this because the torque was already applied at one point in time, and now the two masses are not accelerating?

2. Why does the graph have curves? Does it have to do with gravity changing the speed of the masses?

What I do know is the acceleration of the COM straight down, due to gravity. This can be found by the points on the graph that meet:

It would be awesome if you guys could help me out :)

 

[Orodruin]

Is this because the torque was already applied at one point in time,

The rotation was initiated at the beginning. Gravity itself will give no torque relative to the centre of mass by definition of the centre of mass.

and now the two masses are not accelerating?

Clearly, the masses are changing their velocities and therefore accelerating. However, the rotation remains the same.

2. Why does the graph have curves? Does it have to do with gravity changing the speed of the masses?

No. There is an internal force due to the connection between the masses.

 

[blueblast]

The rotation was initiated at the beginning. Gravity itself will give no torque relative to the centre of mass by definition of the centre of mass.
Clearly, the masses are changing their velocities and therefore accelerating. However, the rotation remains the same.
No. There is an internal force due to the connection between the masses.

What do you mean by internal forces?

 

[Orodruin]

What do you mean by internal forces?

Forces that act between different parts of the system, in this case between the two masses.

 

[blueblast]

Forces that act between different parts of the system, in this case between the two masses.

I don't think I understand what you are talking about. Could you elaborate on the internal forces, and perhaps draw a diagram?

Thanks :)

 

[Orodruin]

There is tension in the bar connecting the masses. The internal forces are the forces mediated by this bar.

 

[blueblast]

So this force causes acceleration, which in turn causes the graph to curve(change velocity), correct?

 

[Orodruin]

Right.

 

[blueblast]

Also, would the tension force count as centripetal force, towards the COM, since the COM is the axis?

 

[jbriggs444]

Also, would the tension force count as centripetal force, towards the COM, since the COM is the axis?

Yes, this force is in the centripetal direction. So it is a centripetal force.

Edit: Some additional explanation may be appropriate here... [hopefully your eyes will not glaze over]

If we consider the two masses and the rod all together as a single closed system then the forces where the masses connect to the rod are "internal" forces. As has been mentioned, a force between two objects is "internal" if both objects are part of the system. Newton's third law then assures us that the force of the one object on the other is equal to the force of the other on the one. The net effect of this third law force pair on the center of mass of the system totals to zero.

A third law force pair has a line of action, but it does not really have a direction. It acts on two objects and acts in the opposite direction on each.

If we are to talk about a particular force as being "centripetal", we are no longer talking about a third law force pair. Instead, we must be talking about only one half of the pair. In this case we are considering the force of rod on mass. In effect, we have focused in on the motion of a single mass and we are no longer considering the entire system. Instead, we are considering a new system consisting of a single mass alone. That single mass is moving in a circle around the center of mass of the "2 mass plus rod" assembly. In this context, the force of rod on mass is an "external" force. It has an unambiguous direction: in toward the center about which this single mass is circling.