Rotational Forces on a Hollow Cylinder

In summary, the conversation discussed modeling a hollow cylinder with known dimensions and density, fixed on a horizontal axle and subjected to a tangential force. The equations used to model the speed of rotation were mentioned, with a focus on the equation for moment of inertia and its use in finding angular acceleration. The linear equation for torque was also mentioned as being similar to the equation for angular acceleration.
  • #1
Ben Reynolds
3
0

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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  • #2
Do you know about moment of inertia... how it is defined, the formula for the MoI of a cylinder, its use in angular acceleration...?
 
  • #3
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.
 
  • #4
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.
 
  • #5
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!
 

1. What is a hollow cylinder?

A hollow cylinder is a three-dimensional shape that consists of two parallel circular bases connected by a curved surface. The curved surface is hollow, meaning it has a hollow space inside.

2. How do rotational forces affect a hollow cylinder?

Rotational forces, also known as torque, can cause a hollow cylinder to rotate around its axis. This rotation can be affected by factors such as the mass distribution of the cylinder, the applied force, and the radius of the cylinder.

3. What is the moment of inertia for a hollow cylinder?

The moment of inertia for a hollow cylinder is a measure of its resistance to rotational motion. It is calculated by taking into account the mass distribution and shape of the cylinder. The moment of inertia for a hollow cylinder is given by I = MR^2, where M is the mass of the cylinder and R is the radius.

4. How does the shape of a hollow cylinder affect its rotational forces?

The shape of a hollow cylinder can greatly affect its rotational forces. A hollow cylinder with a larger radius will have a larger moment of inertia, making it more resistant to rotational motion. Additionally, a hollow cylinder with a more evenly distributed mass will be more stable and have less rotational forces acting on it.

5. What are some real-world applications of rotational forces on hollow cylinders?

Rotational forces on hollow cylinders are commonly seen in everyday objects such as wheels, gears, and flywheels. They are also used in various industrial processes, such as in turbines and engines. Understanding rotational forces on hollow cylinders is crucial in designing and operating these types of systems.

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