How Does Tension Affect Acceleration in a Falling Cylinder?

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Homework Help Overview

The discussion revolves around a physics problem involving a weightless rope tied to a ceiling, with the other end wrapped around a uniform solid cylinder that falls under the influence of gravity. The problem specifically addresses the tension in the string and the acceleration of the cylinder as it descends, incorporating concepts of rotational motion and torque.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants explore the relationship between tension and gravitational force acting on the cylinder, questioning how these forces interact given the cylinder's rotation. There is a focus on the application of torque and its connection to angular acceleration.

Discussion Status

Some participants have provided guidance on the need to consider the forces acting on the cylinder and how torque relates to the problem. There is an acknowledgment of the complexity of the situation due to the rotational dynamics involved. One participant expressed uncertainty about the problem, while another indicated they found a solution.

Contextual Notes

The problem involves understanding both linear and rotational dynamics, and participants are encouraged to review concepts related to torque and rotational motion to fully grasp the situation. The original poster's initial statements and equations set the groundwork for the discussion.

bluejay
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one end of a weightless rope is tied to the ceiling of a building and the other end is wrapped around a uniform solid cylinder that has a radius R and mass M. The cylinder is then released and falls toward the floor. The moment of inertia of a solid cylinder about an axis through its center of mass is: I=0.5MR^2
a. find the tension T in the string?
b. what is the acceleration of M?

Homework Statement


I=0.5MR^2

Homework Equations


T-mg=-ma

The Attempt at a Solution

 
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bluejay said:

Homework Statement


I=0.5MR^2


Homework Equations


T-mg=-ma

You have a start with this, in that you have an equation for the net force on the cylinder as it falls. But this by itself won't get us far because we also need to look at where on the cylinder the forces are acting: this is necessary because the cylinder is rotating as it falls, so there is an additional relationship between T and mg that we will be able to find that will let us solve for all the quantities.

Where do we treat the weight mg as acting on the body of the cylinder? How does the tension T in the string act on the cylinder, and where?
 
I have no idea.
 
You are going to need to review how torques are worked out, because that is the only way you'll be able to solve problems involving rotation.

The linear acceleration a applies to the center of the cylinder; the weight force mg effectively acts there. Since the string is wound around the cylinder, the tension acts along a tangent to the cylinder, so the force T is acting at a distance R (the radius of the cylinder) from the center, about which the cylinder will rotate. The tangent to the cylinder is perpendicular to the radius, so the tension T acts at right angle to that radius. So what torque is the tension applying about the central axis of the cylinder? How does this torque relate to the angular acceleration of the cylinder? (That is where we are going to connect up to the force equation you already wrote.)
 
Never mind i got it. Thanks
 

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