Acceleration of system, connected to a rotational body

[jason lee]

< Mentor Note -- thread moved to HH from the technical physics forums, so no HH Template is shown >[/color]

I have a problem here.
what's the formula for the acceleration of a system wherein.
A disk with a cylinder on top of it with a shaft underneath to wound the thread to connect it with a pulley with a falling mass.
I already got the free body diagram of the falling mass. I have a problem in knowing the diagram for the left side.
we did this in the lab, which the smart timer for acceleration calculated it.
I want to know how did the smart timer get that acceleration through raw formulas. Thanks everyone! :D

 

[jason lee]

Let's say these are the given
M(disk) = 1415.4g
M(ring) = 1428.2g
R(disk) = 11.6cm
R1(ring) = 5.4cm
R2(ring) = 6.4cm
g = 980 cm/s^2
r(shaft) =1.2cm
m = 55g

The smart timer read the acceleration to be 0.4 cm/s^2
i need to get the raw formula for this reading thanks!

 

[jason lee]

< Mentor Note -- thread moved to HH from the technical physics forums, so no HH Template is shown >

I have a problem here.
what's the formula for the acceleration of a system wherein.
A disk with a cylinder on top of it with a shaft underneath to wound the thread to connect it with a pulley with a falling mass.
I already got the free body diagram of the falling mass. I have a problem in knowing the diagram for the left side.
we did this in the lab, which the smart timer for acceleration calculated it.
I want to know how did the smart timer get that acceleration through raw formulas. Thanks everyone! :D

 

[haruspex]

I want to know how did the smart timer get that acceleration through raw formulas.

What exactly is a 'smart timer'? I would have guessed it was physically measuring the movement and calculating the acceleration from that. Its 'formulas' would be based on samples of time and either speed or position.
But from the rest of your post I would have thought that what you wanted was a theoretical calculation of the acceleration based on the set-up. If so, please post an attempt at a solution.

 

[dean barry]

You need to consider the (rotational) moi (moment of inertia) of all the rotating parts, and also express the falling mass also in terms of its effective rotational moi
The force driving the system, you get from the hanging mass.
Don't forget the frictional torque from the bearings.