Rotational Forces on a Hollow Cylinder

AI Thread Summary
To model the rotational speed of a hollow cylinder fixed on a horizontal axle with a tangential force applied, the moment of inertia (I) is crucial. The relevant formula for a cylindrical shell is I = MR^2, where M is the mass and R is the radius. The relationship between torque, moment of inertia, and angular acceleration can be expressed as torque = I * angular acceleration. The mass of the cylinder can be calculated using the formula mass = π * r² * l * ρ. Understanding these equations will help in determining the angular acceleration and rotational speed of the cylinder.
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.
 
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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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