Rotational Dynamics Pulley Problem Help needed

In summary, the conversation discusses a pulley system and finding the accelerations of three masses in order to prevent slipping between the disk and rope. The relevant equations include Newton's second law of motion for translation, rotational and translational equations, and torque about a fixed axis of rotation. The approach to solving the problem involves making guesses at the direction of acceleration and assigning positive directions consistently throughout the equations.
  • #1
1.) Homework Statement
A Pulley System is shown below
Find the accelerations of m1, m2 and m3 (such that there is no slipping between the disk and the rope.)
Assume the threads to be massless.
Drawing.png

Homework Equations


The Relevant equations i think are Newtons 2nd law of motion for translation of m1 and m3

And Rotational as well as Translational equations for m2.
Also Torque about Fixed Axis Of Rotation can be written for m2.

The Attempt at a Solution



[/B]I have attempted the problem like this :-

assumed m1 to go up with acceleration a1,
assumed m2 and m3 both to go up with acceleration a2.
assumed α to be the angular acceleration of the disk anti clockwise.
assumed tensions T1,T2,T3.
T1 is not equal to T2 as the disk has mass.

Drawing_1.png


The other equations are :-
Drawing_1.png
The Variable are a1, a2 , T1, T2 , T3, α
6 equations and 6 variables, so it can be solved.

My Question is that are these equations correct and how do i know that my assumed accelerations are in the correct direction??

Please Reply! Thanks! :smile:
 
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  • #2
In equation (II) there is a handwritten subscript 2 that should be 3.
All else looks good. Are you stuck, or just wanted a progress check?
 
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Likes Sahil Kukreja and bznm
  • #3
Will the answer depend on the direction of angular acceleration or it will come out to be same?
 
  • #4
haruspex said:
In equation (II) there is a handwritten subscript 2 that should be 3.
All else looks good. Are you stuck, or just wanted a progress check?

thanks, yes that's a typo.
I wanted to know if my direction of accelerations and angular acceleration are correct or not?
 
  • #5
Sahil Kukreja said:
thanks, yes that's a typo.
I wanted to know if my direction of accelerations and angular acceleration are correct or not?
I cannot tell since you have not posted your solution of the equations.
The directions you choose for the variables at the start is immaterial. All you do there is choose which direction is positive for that variable. If it turns out that the accekeration is in that direction you will get a positive answer. If it is the other way you will get a negative answer.
There are generally three approaches:
- In the "naive" approach, you make a genuine guess at which way each object will accelerate and pick the positive directions accordingly;
- in what one might call the Cartesian approach, you stick to a convention like up is positive and right is positive. But in general some accelerations could be at an angle, so you then have to break it into components.
- Assign the positive directions at random.
Or you could use a hybrid.
Whichever you choose, the important thing is to be consistent through the equations.
 

1. What is rotational dynamics and how does it apply to a pulley problem?

Rotational dynamics is the study of rotational motion, specifically the motion of objects that rotate around a fixed axis. In a pulley problem, rotational dynamics applies when a rope or cable is wrapped around a pulley and there is a force acting on one side of the rope, causing the pulley to rotate.

2. What is the relationship between torque and angular acceleration in a pulley problem?

Torque is the rotational equivalent of force, and it is the product of force and the distance from the axis of rotation. In a pulley problem, the torque applied to the pulley is directly proportional to the angular acceleration, meaning that a larger torque will result in a larger angular acceleration.

3. How can I determine the tension in the rope in a pulley problem?

In order to determine the tension in the rope, you can use the equations of rotational dynamics, specifically the equation for torque. By setting the net torque equal to the product of the mass and angular acceleration, you can solve for the tension in the rope.

4. What is the difference between a fixed pulley and a movable pulley in a rotational dynamics problem?

A fixed pulley does not rotate, and therefore does not contribute to the rotational dynamics of the system. A movable pulley, on the other hand, can rotate and can affect the dynamics of the system by changing the direction and magnitude of the tension in the rope.

5. How can I apply the concept of conservation of energy in a pulley problem?

In a pulley problem, the concept of conservation of energy can be applied by considering the potential energy and kinetic energy of the system. The work done by the forces acting on the system is equal to the change in the total energy of the system, and this can be used to solve for unknown quantities such as the final velocity of an object attached to the pulley.

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