Rotational Forces on a Hollow Cylinder

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Homework Help Overview

The discussion revolves around modeling the rotational dynamics of a hollow cylinder subjected to a tangential force. The cylinder's characteristics, including its radius, length, and density, are specified, and the context involves understanding angular velocity and acceleration in relation to applied forces.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to identify relevant equations for modeling the cylinder's rotation, expressing uncertainty about angular velocity and moment of inertia. Participants discuss the definition and application of moment of inertia, particularly for a cylindrical shell, and explore how it relates to angular acceleration.

Discussion Status

Participants are actively engaging with the concepts of moment of inertia and torque, with some guidance provided on the relationship between torque, moment of inertia, and angular acceleration. There is an ongoing exploration of how to apply these concepts to the problem at hand.

Contextual Notes

The original poster notes a lack of familiarity with angular velocity and expresses difficulty in finding applicable equations, which may influence the direction of the discussion.

Ben Reynolds
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Homework Statement


I am trying to model a hollow cylinder of known radius r, length l and density rho.
The cylinder is fixed on a horizontal axle along its longest axis (l) and will have a force F applied tangentially to its surface and perpendicular to its axis, with negligible frictional forces acting between it and the axle.
What equations could I use to model the speed of its rotation?

Homework Equations


Mass = pi*r2*l*rho
Some equation involving moments, potentially?
I am a mathematician and have little work on angular velocity, so I apologise for the trouble.

The Attempt at a Solution


I have attempted to find a relevant equation but all searches gave either inapplicable scenarios or equations quoted ad verbatim with no clarification to notation.
 
Physics news on Phys.org
Do you know about moment of inertia... how it is defined, the formula for the MoI of a cylinder, its use in angular acceleration...?
 
Okay, so I have found the equation I = MR^2 for a cylindrical shell of negligible width being rotated along its long axis, which is close to what I'm looking for. However, I would not know how to include such an equation in finding angular acceleration.
 
Ben Reynolds said:
Okay, so I have found the equation I = MR^2 for a cylindrical shell of negligible width being rotated along its long axis, which is close to what I'm looking for. However, I would not know how to include such an equation in finding angular acceleration.
It's very like the linear equation: torque about axis = moment of inertia about axis * angular acceleration about axis.
 
haruspex said:
It's very like the linear equation: torque about axis = moment of inertia about axis * angular acceleration about axis.

That's perfect, thanks!
 

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