Maths required for rotation point

[karen_lorr]

Hi

The first thing to say about this is that I don’t have a clue where to start.

What I’m looking for is somewhere (maybe a website or just a brief introduction) I can study – and learn – about the forces involved and the maths required.

_______

Say I have an item/length/beam/weight/etc (C in the graphic) that can rotate about a point (B in the graphic) which is supported on an unmovable base (A in the graphic).

C can be heaver, taller, have more mass, etc, etc (it can change) although it’s rotation point never changes

What I’m looking for is a way to work out how the properties of C will affect the force required to rotate it around point B.

This is not a homework question (I left school over 40 years ago), it’s just for my own personal interest and education.

Thank you

Here is the graphic (on Microsoft Onedrive). I have put this link as well in case you can't see it.
https://1drv.ms/i/s!AlXOOGaTv36QgQ4hlbbk4IQpmTEX

 

[DoItForYourself]

Hi,

I think you should start comparing the equations of linear motion with the respective of rotational motion. You can study some basic equations in this website: https://www.4physics.com/phy_demo/Newton/Newton_rot.htm.

Let's consider this system to be horizontal and the air resistance to be negligible. There is no force exerted on this system initially (no gravity-horizontal system). In this case, the moment of inertia (I) changes when we change the geometry of c. For example if c is a uniform cylinder with radius R and length l and is rotating around b, then: I=(MR^2/4)+(Ml^2/3) where M is the mass of c.

So you must follow these steps:
1) Decide the rotational acceleration (a=dω/dt) with which you want c to start rotating.
2) Calculate the moment of inertia (I) based on the geometrical characteristics of your system.
3) From the equation Στ=Fr=Ia, you can calculate the Force that needs to be exerted on a specific point of the object c.

Have in mind that τ=Fr, where F is the force exerted on the cylinder and r the distance of the point (in which F is exerted) from b.

The difficult step is to calculate the moment of inertia for non-uniform objects, because you need to use the integral of (r^2 dm).