Solving Rotation Homework: Answers & Explanations

[physicalerror]

Hey, guys, can you lend me a hand with this problem? I wrote out some solution but it seems way too short and obvious so I am worried that my logic might be wrong. Thank you all for the input.

A rope is coiled around a homogeneous circular disk of mass m=20 kg and radius R=0,5 m. The disk starts rotating when it falls down with the rope being unwinded. One end of the rope is attached to a hook in the ceiling.

a) What kind of motion does the center of the circular disk perform?
b) What is the angular acceleration and the linear downward acceleration of the disk?
c) What is the force exerted on the hook while the disk falls down?

Here is what I get:
a) linear uniform motion
b) angular acceleration = 39,24 rad/s^2; linear acceleration = 19,62 m/s^2
c) force = 196,2 N

Totally wrong, no?

(Initially I accidentally posted this in the wrong section. Sorry!)

 

[thejinx0r]

What are the equations that you are using?

Anyways,
A safe sanity check is that for any object on Earth, if it is just falling, then the linear acceleration cannot be greater than 9.81 m/s^2

 

[physicalerror]

b) M=I*E=F*R where E denotes angular acceleration
=> 0,5*m*R^2*E=m*g*R => E=2*g/R=39,24 rad/s^2

a=R*E=19,62 m/s^2

c) T=G=m*g=196,2 N

 

[physicalerror]

Any ideas, anyone? Many thanks!