Rotational problem

  • Thread starter MikkelR
  • Start date
  • #1
1
0
I'm kinda stuck in this mechanical problem, ill try to describe the situation.

A plane, homogeneous disk may slide on a frictionless horizontal table. A cord is fastened to the disc and wrapped many times around the rim of the disc. The cord goes without friction through a small eyelet at the edge of the table and is connected to a mass m. The mass of the disc is M and its radius is R. The system is started from rest and the cord is assumed to be taut throughout the motion. Ignore the mass of the cord.

http://ylle.eu/DSC00602.JPG (my sketch of the problem)

Describe the velocity of the disc as a function of time.

Here is what i have computed of equations so far.

The forces affecting the disc M must be M(d²x)/(dt²) = mg
The forces affecting the mass m must be m(d²x)/(dt²) = mg - S

The torque(N) exerted on M can be described as

N = mgR

The moment of inertia for a circular disk around its CM is

I = (1/2)MR²

The angular momentum is

L = Iw

Torque equals the change of angular momentum with respect to time

N = Iw'
N = (1/2)MR²w'
mgR = (1/2)MR²w'

And from this point i cant really seem to maky any more observations that can help me solve the problem.
I hope someone can clarify the problem for me

Thanks in advance
Mikkel
 

Answers and Replies

  • #2
OlderDan
Science Advisor
Homework Helper
3,021
2
You need to rethink the force acting on the disk. Look at what you did for the hanging mass and think about the connection between the two objects.
 

Related Threads on Rotational problem

  • Last Post
Replies
2
Views
8K
  • Last Post
2
Replies
28
Views
1K
  • Last Post
Replies
4
Views
1K
  • Last Post
Replies
4
Views
892
  • Last Post
Replies
8
Views
2K
  • Last Post
Replies
4
Views
926
  • Last Post
Replies
15
Views
680
  • Last Post
Replies
17
Views
13K
  • Last Post
Replies
5
Views
1K
  • Last Post
Replies
4
Views
3K
Top