A disk on a slippy surface (Rotation and Translation)

[srecko97]

Homework Statement

There is a disk with mass 50 grams put on a slippy surface (no friction!). Its radius is 5 cm. Mass of the weight is 20 grams. At the beginning there is no motion. How far does the center of mass of the disk move in 10 seconds? (answer: 91 m) How many turns does the disk in 10 seconds?

Homework Equations

F=ma
F*r = J*alpha

The Attempt at a Solution

The only force on the disk is the force of the rope if there is no friction. -->

I did not solved the second question as the first answer is wrong. Please help me, correct me.

 

[TSny]

Is the acceleration of the center of the disk the same as the acceleration of the hanging weight?

 

[srecko97]

Yeah, right, they are not. But I do not know how to solve it in other way

 

[srecko97]

acceleration of the disk = force of the rope / mass of the disk ... Is that correct?

 

[TSny]

acceleration of the disk = force of the rope / mass of the disk ... Is that correct?

Yes. ("Acceleration of the disk" means the acceleration of the center of the disk.)

 

[srecko97]

Yes, I meant that

 

[TSny]

You will need to relate the acceleration of the hanging weight to the acceleration of the center of the disk and the angular acceleration of the disk.

 

[srecko97]

angular acceleration (alpha) = (2 * force_rope )/ (mass * radius)

 

[srecko97]

yeah,yeah, i think i got it! circimferential acceleration + acceleration of center of mass = acceleration of weight , right?

 

[srecko97]

Ok, thanks, I got the right result! Your hints are very useful! Can you give me your phonenumber? ... just joking! have a nice day, thanks!

 

[TSny]

yeah,yeah, i think i got it! circimferential acceleration + acceleration of center of mass = acceleration of weight , right?

Ok, thanks, I got the right result! Your hints are very useful! Can you give me your phonenumber? ... just joking! have a nice day, thanks!

Good work!

 

[Frodo]

I have been struggling with as a recreational, not homework problem.

Does the disk rotate? If so, about which axis does it disk rotate? And why?

I can make three arguments but cannot see which is correct.

1. The disk rotates about its centre

2. The disk rotates about the point opposite to where the rope leaves the disk. I prefer this argument. It is smilar to the wheel on a car which, when viewed from a frame attached to the ground (as we have here), rotates about its point of contact with the ground. If there was friction then this is the intuitive answer.

3. The disk does not rotate because there is only one force acting on it. I can draw a box enclosing the disk and the rope is then applying the only external force to the system.

I tried simplifying the problem to a stick on a table with friction which will then rotate about the far end of the stick and is how I came to argument 2. But why would it rotate if there was no friction - why isn't it just pulled along without rotation? Replacing the rope with a little rocket didn't help.

Any guidance will be welcomed. It's two years old so any answer shouldn't be a spoiler.

 

[berkeman]

I have been struggling with as a recreational, not homework problem.

Does the disk rotate? If so, about which axis does it disk rotate? And why?

I can make three arguments but cannot see which is correct.

1. The disk rotates about its centre

2. The disk rotates about the point opposite to where the rope leaves the disk. I prefer this argument. It is smilar to the wheel on a car which, when viewed from a frame attached to the ground (as we have here), rotates about its point of contact with the ground. If there was friction then this is the intuitive answer.

3. The disk does not rotate because there is only one force acting on it. I can draw a box enclosing the disk and the rope is then applying the only external force to the system.

I tried simplifying the problem to a stick on a table with friction which will then rotate about the far end of the stick and is how I came to argument 2. But why would it rotate if there was no friction - why isn't it just pulled along without rotation? Replacing the rope with a little rocket didn't help.

Any guidance will be welcomed. It's two years old so any answer shouldn't be a spoiler.

There's actually a current thread on this problem, I believe:

https://www.physicsforums.com/threads/rotation-of-a-rigid-body.990335/