How Do You Calculate Tension and Acceleration in a Rotating Cylinder System?

In summary, the problem involves a uniform solid cylinder of mass M and radius R rotating on a frictionless horizontal axle. Two equal masses are connected to the cylinder via light cords and the system is released from rest. The summary includes the equations used to find the tangential acceleration and the tension in the cords. The net torque on the cylinder is found to be 2TR and the relation 4T/M=a, where T is the tension in each cord and a is the acceleration. The final step is to solve for T and a using the equations T=(mg-ma) and a=(TR^2)/(1/2mr^2).
  • #1
Tlocc
14
0

Homework Statement


A uniform, solid cylinder of mass M and radius R rotates on a frictionless horizontal axle. Two equal masses hang from light/weightless cords wrapped around the cylinder. If the system is released from rest, find:
A. The tension in each cord.
B. The acceleration of each mass after the masses have descended a distance of H.


Homework Equations


Torque=T(tension)R
Torque=I x Alpha
T=mg-ma
T=Torque/R
Alpha=A(tangential)\R
I=((1/2)mr^2)


The Attempt at a Solution


Based on the relevant equations, I deduced that the tangential acceleration is the downwards acceleration since it is perpendicular to the radius. Combining equations as follows I retrieved my findings for a.
T=(I x Alpha)\R
TR=(I x Alpha)
TR=(Ia)\R
TR^2=Ia
(TR^2)\I=a
(TR^2)\((1\2)mr^2)=a
(2T)\m=a

I don't know what the answer is as it is not in the back of the book nor was it given during class so I don't know how far or close I am to the answer. If I'm right, let me know. If I'm wrong, it would be greatly appreciated if you could show me where I went wrong or if I was forgetting something.
 
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  • #2
Hmm I'm wondering why nobody answered me and also a quick comment:
I'm not sure if this acceleration would be constant or not..
 
  • #3
If two masses are equal why will they move at all?
 
  • #4
the two equal masses are hanging from the big mass
 
  • #5
The cylinder (Mass M) is rotating on a fixed axis and the equal masses are connected at the ends of a rope wrapped around the cylinder. So why should the masses move. If the masses were unequal, the heavier one would move down.
 
  • #6
they aren't attached to the same cord
 
  • #7
there are two separate cords
 
  • #8
In that case what you have done is basically correct except that there are two cords carrying equal weights, hence equal tensions T. Net torque on the cylinder will be 2TR and the relation will be 4T/M = a. Solve this one and mg - T = Ma to get T and a. a will be constant. Is B) finding acceleration or is it velocity?
 
  • #9
B was finding acceleration which was what my attempt was because I found T via the relevant questions.
 

FAQ: How Do You Calculate Tension and Acceleration in a Rotating Cylinder System?

What is a tough rotational motion problem?

A tough rotational motion problem is a physics problem that involves the study of rotational motion, such as the motion of objects spinning or rotating around a fixed axis. These problems often require a deep understanding of concepts such as torque, angular momentum, and rotational inertia.

What are some common examples of tough rotational motion problems?

Some common examples of tough rotational motion problems include the motion of a spinning top, the rotation of a bicycle wheel, and the motion of a planet around the sun. These problems can also be found in engineering and mechanics, such as calculating the torque on a gear or determining the angular momentum of a rotating machine.

What are the key concepts to understand in order to solve a tough rotational motion problem?

In order to solve a tough rotational motion problem, it is important to have a strong understanding of concepts such as angular velocity, angular acceleration, moment of inertia, and the relationships between these quantities. You should also be familiar with the equations and principles of rotational motion, such as Newton's second law for rotational motion and the conservation of angular momentum.

How can I approach solving a tough rotational motion problem?

One approach to solving a tough rotational motion problem is to break it down into smaller, more manageable parts. This may involve drawing diagrams, identifying known and unknown quantities, and applying relevant equations and principles. It can also be helpful to use vector notation to keep track of direction and use units consistently throughout your calculations.

What resources are available to help me solve tough rotational motion problems?

There are many resources available to help you solve tough rotational motion problems, including textbooks, online tutorials, and practice problems. You can also seek help from a teacher, tutor, or study group to work through problems together. It is important to actively engage with the material and practice solving problems in order to improve your understanding and problem-solving skills.

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