Rotating disk falling from string problem

[sAXIn]

Problem Sketch

Okay so this is the problem the upper disk will be of M1 mass and R1 radius
both disk are solid so I(oe)=1/2MR^2 , the second disk will be HM2 , HR2.
After system is left from rest I understand that the lower disc will start rotating and going down from the rope also it has linear acceleration down because the string is going down from upper disc.

I wrote sigma tau for both discs and sigma Y for the lower one but I need to express TA, Alfa 1 , Alfa 2 and A2 (linear acceleration of second disc)
(alfa -=> angular acceleration )! all of them should be written without being expressed by others.
I can't also figure out why when I express alfa2 by sigma moments on point where the string is leaving the disc it isn't equal to alfa2 by sigma moments on center of disc.

Thank's in advance for help .

 

[OlderDan]

Problem Sketch

Okay so this is the problem the upper disk will be of M1 mass and R1 radius
both disk are solid so I(oe)=1/2MR^2 , the second disk will be HM2 , HR2.
After system is left from rest I understand that the lower disc will start rotating and going down from the rope also it has linear acceleration down because the string is going down from upper disc.

I wrote sigma tau for both discs and sigma Y for the lower one but I need to express TA, Alfa 1 , Alfa 2 and A2 (linear acceleration of second disc)
(alfa -=> angular acceleration )! all of them should be written without being expressed by others.
I can't also figure out why when I express alfa2 by sigma moments on point where the string is leaving the disc it isn't equal to alfa2 by sigma moments on center of disc.

Thank's in advance for help .

The upper disk only rotates, with angular acceleration resulting from the applied torque resulting from the tension in the string. The lower disk accelerates downward responding to the force of gravity less the tension in the string. It also rotates about its center because the tension results in a torque about the center. The thing the two disks have in common is the tension in the string. It sounds like you have written equations for these things. There is an additional connection between these three motions having to do with their displacements. Think about the distance the center of the lower disk has moved in terms of the angular displacements of the two disks.

 

[thepatientmental]

The problem sketch provided is a classic example of a rotating disk falling from a string problem. In this problem, there are two disks - an upper disk with mass M1 and radius R1, and a lower disk with mass M2 and radius R2. Both disks are solid, meaning they have a moment of inertia of 1/2MR^2. The system is initially at rest, and the lower disk is attached to the upper disk by a string.

As the system is released, the lower disk starts rotating and falling down due to the linear acceleration of the string pulling it down. To solve this problem, the author correctly notes the need to use torque equations (sigma tau) for both disks and a force equation (sigma Y) for the lower disk. The goal is to find the angular acceleration (alfa) and linear acceleration (A2) of the second disk without using any other variables.

However, the author mentions difficulties in expressing TA, alfa1, alfa2, and A2 without using other variables. It is important to note that in order to solve this problem, it is necessary to use the relationships between torque, angular acceleration, and linear acceleration. These relationships can be seen in the equations for torque (tau = I*alfa) and linear acceleration (A = R*alfa), where I is the moment of inertia and R is the distance from the axis of rotation. Therefore, it is not possible to express all variables without using others.

Additionally, the author raises a valid question about the difference between expressing alfa2 using the sigma moments at the point where the string leaves the disk and at the center of the disk. This is because the point where the string leaves the disk is not the center of rotation for the second disk. In order to accurately solve this problem, it is important to choose a consistent point of reference for calculating moments and to use the correct equations for each disk.

Overall, this is a challenging problem that requires a thorough understanding of torque, angular acceleration, and linear acceleration. It is important to carefully consider all variables and their relationships in order to accurately solve the problem.