Find the Angular Acceleration with and Without the disk inertia

  • #1
249
1

Homework Statement


Determine the angular acceleration of the uniform disk if (a) the rotational inertia of the disk is ignored and (b) the inertia of the disk is considered. The system is released from rest, the cord does not slip on the disk, and bearing friction at O may be neglected. The angular acceleration is positive if counterclockwise, negative if clockwise.

I have attached an image of the question


Homework Equations





The Attempt at a Solution



m1 = 1.5 kg
m2 = 3.1kg
r = 0.32m

I started by summing the moments about O

ƩMO = (-m1gr + m2gr)/IO

IO = 2mr2 but I'm not sure why this is the case. A classmate of mine said something about adding in the inertias from the weight but I'm not sure what this means.

Also, how to I account for the disk inertia?

Any advice would be appreciated.
 

Attachments

Answers and Replies

  • #2
Simon Bridge
Science Advisor
Homework Helper
17,857
1,655
I started by summing the moments about O
... which confused you.

The force on the disk comes from the tensions acting at opposite points.
The tensions come from the weights. The equation is ƩM = Iα ... which is not the same as:
ƩMO = (-m1gr + m2gr)/IO
Breaking it down:

In the first case you would be better to find the linear acceleration of the weights, and use that to deduce the angular acceleration of the disk.

In the second case, you have three free-body diagrams instead of just two.
You need ƩF=ma as well as ƩM = Iα
 

Related Threads on Find the Angular Acceleration with and Without the disk inertia

  • Last Post
Replies
13
Views
1K
Replies
1
Views
11K
Replies
4
Views
2K
Replies
6
Views
5K
Replies
4
Views
1K
Replies
1
Views
765
Replies
2
Views
3K
  • Last Post
Replies
3
Views
997
  • Last Post
Replies
2
Views
4K
Replies
7
Views
2K
Top