# Acceleration of system, connected to a rotational body

• jason lee
In summary, the smart timer calculates the acceleration of the system by taking into account the rotational moi of all the rotating parts, the force driving the system, and the frictional torque from the bearings.
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

Last edited by a moderator:
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 said:
< 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

jason lee said:
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.

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.

## What is the acceleration of a system connected to a rotational body?

The acceleration of a system connected to a rotational body is the rate of change of the rotational velocity. It is also known as angular acceleration and is measured in radians per second squared.

## How does the mass of the system affect its acceleration?

The mass of the system does not affect the acceleration of a rotation. Instead, it affects the amount of force needed to generate the acceleration. The greater the mass of the system, the more force is required to produce the same amount of acceleration.

## What is the difference between tangential and centripetal acceleration?

Tangential acceleration is the component of acceleration that is tangent to the circular path of the system. It is responsible for the change in the magnitude of the velocity. Centripetal acceleration, on the other hand, is the component of acceleration that points towards the center of the circular path. It is responsible for keeping the system moving in a circular motion and preventing it from flying off in a straight line.

## Does the distance from the center of rotation affect the acceleration of a system?

Yes, the distance from the center of rotation does affect the acceleration of a system. The further away the system is from the center of rotation, the greater the tangential acceleration and the smaller the centripetal acceleration. This is because the distance affects the length of the circular path and the speed of the system.

## How is the angular acceleration related to the moment of inertia?

The angular acceleration of a system is directly proportional to the torque applied to it and inversely proportional to its moment of inertia. The greater the moment of inertia, the smaller the angular acceleration for the same amount of torque. This is because the moment of inertia represents the resistance of the system to rotational motion.

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