Rigid Body Rotational or Translational ?

In summary, the problem involves three masses, A, B, and C, with A having a mass of 4 kg and B and C being identical uniform discs with a mass of 2 kg each. The string supporting A is ideal. The question asks for the acceleration of A. C is free to move up and down as well as rotate, making the problem more complex. The axle of B is fixed while the axle of C is not, indicating that C only has translational motion. The accelerations of A and C are not the same, so the relationship between the lengths of the rope (ratios) must be used to solve the problem. It is important to work out the kinematics carefully before attempting to solve the problem
  • #1
TheRedDevil18
408
1
Capture.jpg

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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  • #2
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.
 
  • #3
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
 
  • #4
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.
 
  • #5
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.
 
  • #6
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 ?
 
  • #7
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.
 
  • #8
Did you see my original reply where I said
Dr.D said:
move up and down as well as rotate

?
 
  • #9
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 :)
 

1. What is the difference between rotational and translational motion for a rigid body?

Rotational motion refers to the movement of a rigid body around an axis, while translational motion refers to movement along a straight line. In rotational motion, all points of the rigid body move in circular paths, while in translational motion, all points move in parallel paths.

2. How do you calculate the rotational and translational motion of a rigid body?

The rotational motion of a rigid body can be calculated using the formula θ = s/r, where θ is the angle of rotation, s is the arc length, and r is the radius of rotation. The translational motion can be calculated using the formula s = v*t, where s is the distance traveled, v is the velocity, and t is the time.

3. What is the moment of inertia for a rigid body?

The moment of inertia is a measure of a rigid body's resistance to rotational motion. It is calculated by summing up the products of the mass of each particle of the body and the square of its distance from the axis of rotation.

4. How does the distribution of mass affect the rotational and translational motion of a rigid body?

The distribution of mass plays a significant role in the rotational and translational motion of a rigid body. A body with a higher mass concentrated towards its center of mass will have a lower moment of inertia and will be easier to rotate. On the other hand, a body with a higher mass distributed away from its center of mass will have a higher moment of inertia and will be harder to rotate.

5. What are some real-life examples of rigid body rotational and translational motion?

Some examples of rotational motion include the spinning of a top, the movement of a Ferris wheel, or the rotation of the Earth on its axis. Examples of translational motion include the movement of a car on a straight road, the flight of an airplane, or the movement of a person walking in a straight line.

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