# Homework Help: Confusing ROTATIONAL RIGID BODY QUESTION problem conceptualizing

1. Nov 3, 2008

### avenkat0

1. The problem statement, all variables and given/known data
A piece of cloth with irrelavent mass is wrapped around a 67.5 kg cylinder of radius 0.167 m. Joe holds the free end of the cloth. The cylinder is released from rest, and Joe pulls the tape upward at a speed that just prevents the center of mass of the cylinder from falling as the tape unwinds. Assume:
- the cylinder is always parallel to the floor
- the tape is always perpendicular to the radius of the cylinder
- the tape does not slip over the cylinder

a) Find the magnitude of the tension in the tape as the cylinder turns.

2. Relevant equations

3. The attempt at a solution
I have no idea where to start... I dont think i quite understand it conceptually... like i dont quite see the picture in my head

Last edited: Nov 3, 2008
2. Nov 3, 2008

### Staff: Mentor

If the cloth isn't pulled up, it will just unwind as the cylinder falls. (Imagine a heavy log rolled up in a carpet and you let it unwind.)

To answer the question, apply Newton's 2nd law. What forces act on the cylinder?

3. Nov 3, 2008

### avenkat0

is it kind of like the logs that are floating on the water while people run on it... thus in turn staying in the same place?...
so the cloth is giving the cylinder a torque to equal its fall? making the center of mass stay at the same place?

4. Nov 3, 2008

### Staff: Mentor

Something like that.
The cloth is certainly exerting a torque on the cylinder.
Yes, the cloth is being pulled up fast enough that the center of mass doesn't move.

5. Nov 3, 2008

### avenkat0

should the tension in the cloth equal mg down since the tension keeps it from falling down?
I keep confusing linear qualities with rotational qualities!....

6. Nov 3, 2008

### Staff: Mentor

Sounds good to me.

7. Nov 3, 2008

### avenkat0

Thank you so much... One more thing...
c) Find the length of the cloth that has been unwound when the cylinder reaches an angular speed of 28.3 rad/s

I found the work done was 376.92 J...
Now i set Delta Theta = 376.92/Tourque...
i.e 376.92/I(alpha)
but how would i go about finding alpha?

because if i find alpha cant i find Theta and then 2pi (Theta) should be the length the cloth unwinds right?

8. Nov 3, 2008

### Staff: Mentor

To find alpha, use Newton's 2nd law for rotation. Then you can use kinematics to find theta and then the length. (No, 2pi(theta) is not the length.)

But if you've already found the work done, there's no need to find alpha or theta.

9. Nov 3, 2008

### avenkat0

hmmm work done is torque(distance)... But I don't have the tension either how would I go about findig the distance?

I tried using I(alpha)=torque and then omega final and omegia0 is 0 but I'm missing theta time and alpha so I wasn't able to find alpha using kibematics...

Have I overlooked something??

Again Thank you

10. Nov 3, 2008

### Staff: Mentor

Careful. Work is force*distance (or torque*angle).
Sure you have the tension. That was the first thing you solved for.
Look for a kinematic formula that relates speed and distance, not time.