Suggestions:The problem is a bit more involved than what might first appear. However, the general process is the same as for all of our other problems.
Velocity problem
- F is the IC for the wheel on the right. Use this to see that the speed of A is twice that of C.
- A and B have the same speed (straight, inextensible cable connecting them).
- E is the IC for the wheel on the left. Use this to find the angular speed of the wheel on the left.
Acceleration problem
- Note that F is a zero horizontal component of acceleration (no slip). Use this to find the angular acceleration of the wheel on the right.
- Use the results from 1. above to find the horizontal component of acceleration for A.
- A and B have the same horizontal component of acceleration.
- E has a zero horizontal component of acceleration (no slip). Use this to find the angular acceleration of the wheel on the left as well as the acceleration of point O.
- Write the acceleration of D in terms of the now-known acceleration of point O.
8 comments:
is the last step [a(d) = a(o) + alpha(e) x r(do) - w(e)^2 x r(do)]?
thats the relationship I used. Also, is it correct that at point O, O only has an i component of acceleration?
I'm having trouble finding the angular acceleration of the right wheel. I use the acceleration equation of C with respect to F and I end up with one term in terms of j and two unknowns in terms of i. This basically means I have one equation with two unknowns.
Is it not possible to solve for a(d) without knowing the acceleration of point O.
In other words, coudn't you find the angular acceleration of the left disk and use the known acceleration of point B to solve for a(d)?
Zachk, remember that A_f has no horizontal component of acceleration because of no slipping (#1 in the acceleration hints). That should make one of your unknowns be equal to the j component.
-leonardo c.
How does it help knowing that the horizontal components of acceleration for A and B are the same.
Let me give some of your questions a try:
--steve-o
You are correct; O moves along a straight horizontal path. Therefore, O can NOT have a vertical component of acceleration.
--zachk
As Peter says below, the no-slip condition at F says that the x-component of a_F is zero. Your acceleration equation should have two unknowns: a_Fy and alpha (ang. acc. of wheel on right). Solve these two scalar equations.
--vincent lingle-munos
You cannot go directly from B to D. One reason is that you do not know the y-component of the acceleration of B (only the x-component is the same as that of a_A). Also, you need to include O and E in some way to find the alpha for the wheel on the left.
--peter merrick
You need to find the angular acceleration of the wheel on the left. Knowing that the x-components of the acceleration of A and B are equal helps in determining this angular acceleration.
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