Rigid Body Rotational or Translational ?

[TheRedDevil18]

In the figure A has mass 4 kg. B and C are identical uniform discs, each of mass 2 kg. The
string supporting A is ideal. Obtain the acceleration of A

I have just one question, Why is pulley C undergoing translational motion ?, it should be rotational motion because it rotates about a fixed axis

 

[Dr.D]

I don't see anything in the problem statement that says C rotates about a fixed axis. Where do your read that?

Actually, I think that C is free to move up and down as well as rotate, and this is what make the problem interesting.

 

[TheRedDevil18]

I don't see anything in the problem statement that says C rotates about a fixed axis. Where do your read that?

Actually, I think that C is free to move up and down as well as rotate, and this is what make the problem interesting.

So how would you know, would you just assume it's translational ?, or is their some way of figuring it out ?, maybe the question is too vague ?, because in the memo it's translational. Also, how do you know the accelerations aren't the same ?, because you supposed to use the relationship between the lengths of the rope to get the accelerations

 

[Dr.D]

B shows a support from the overhead to the axle of B. C does not show anything of this sort. This indicates that the axle of B is fixed while the axle of C is not.

 

[SteamKing]

Well, pulley B is obviously fixed to the overhead. If pulley C were also secured to a fixed axle, then the mass A would just be suspended, as there could be no relative movement between the two sheaves. In working out physics problems, sometimes your imagination gets as much a workout as your intellect.

 

[TheRedDevil18]

B shows a support from the overhead to the axle of B. C does not show anything of this sort. This indicates that the axle of B is fixed while the axle of C is not.

Oh yes I see that, but then it would be translational and rotational motion ?, then why is it strictly translational ?

 

[SteamKing]

Oh yes I see that, but then it would be translational and rotational motion ?, then why is it strictly translational ?

The pulley C is not going to rotate about anything except its own axis, and its axis is going to move up and down as the mass A changes position, so the motion of the center of C is translational. The mass A can only move up and down, so its motion is translational.

The problem asks for the acceleration of A. If the problem had asked instead for the acceleration of a point on the periphery of pulley C, then you would need to know something about the rotational motion of that point about the axis of the pulley.

 

[Dr.D]

Did you see my original reply where I said

move up and down as well as rotate

?

 

[TheRedDevil18]

Oh yes, sorry guys, its rotating and moving up and down so rotational and translational motion

One more question, the accelerations aren't the same, right ?, so I have to use the relationship between the length of the rope (ratios) ?

 

[Dr.D]

Work out the kinematics carefully before you try to do the rest. If you have the kinematics well in hand, the rest will be easy; if not, you are not likely to ever get the problem correct.

 

[TheRedDevil18]

Ok, thanks guys :)