Rigid Body Rotational or Translational ?

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SUMMARY

The discussion centers on the dynamics of a system involving mass A (4 kg) and two identical uniform discs, B and C (each 2 kg). Participants clarify that pulley C undergoes both translational and rotational motion, as it is free to move vertically while rotating about its own axis. The key takeaway is that the accelerations of mass A and pulley C are not the same, necessitating the use of rope length relationships to determine the correct kinematics for solving the problem.

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  • Understanding of Newton's laws of motion
  • Familiarity with kinematics and acceleration concepts
  • Knowledge of rotational dynamics and fixed versus free axles
  • Ability to analyze pulley systems in physics
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  • Study the principles of rotational dynamics in pulley systems
  • Learn how to apply Newton's laws to complex systems with multiple masses
  • Explore kinematic equations and their applications in pulley problems
  • Investigate the relationship between linear and angular acceleration
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Students and educators in physics, mechanical engineers, and anyone interested in understanding the dynamics of pulley systems and motion analysis.

TheRedDevil18
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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
 
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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.
 
Dr.D said:
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
 
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.
 
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.
 
Dr.D said:
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 ?
 
TheRedDevil18 said:
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.
 
Did you see my original reply where I said
Dr.D said:
move up and down as well as rotate

?
 
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) ?
 
  • #10
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.
 
  • #11
Ok, thanks guys :)
 

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