A few suggestions on this problem:
- It is recommended to use the instant center method to find angular velocities of the wheels.
- For no-slip motion, points F and E in the above figure are the instant centers for the two wheels. Use E to find the angular velocity of the wheel on the right as well as the speed of point A.
- Note that the speed of A is equal to the speed of B.
- Use F to find the angular velocity of the wheel on the right.
- Now use the rigid body acceleration equation to relate the acceleration of E to the known acceleration of C. (Note that E has only a vertical component of acceleration due to the no-slip condition.). This will give the angular acceleration of the wheel on the right. Then use the rigid body acceleration equation between C and A to find the acceleration of point A.
- Note that the horizontal component of the acceleration of A is the same as the horizontal component of acceleration of B.
- Use the acceleration equation between F and B to find the angular acceleration of the wheel on the left. (Again, F has only a vertical component of acceleration.)
- Finally, use the acceleration equation between F and D to find the acceleration of D.
A few suggestions on this problem:
6 comments:
My final equation for the acceleration of D is dependent on F for the i component. I went back through my equations and couldn't find any way to find either variable. Please help.
The acceleration of F should be 0 because since it is just in the j direction its never moving away from the surface of the ground.
Wouldn't point F have an acceleration to the center though? I am at the same point of having an equation of acceleration between F and D, but it is dependent on the acceleration at point F. Any ideas?
You get a_f from the a_b equation, and it's in the positive y direction. From there, just plug it into the a_d equation and chug along to the final answer. a_f is zero only in the x-direction.
a_b i = a_f j + (-alpha k X r_b/f j) - (w^2)(r_b/f) j
-alpha k X r_b/f evaluates to +i
Knowing j should be zero for a_b, solve away.
Please correct me if I did anything wrong.
Another option you have is to use equations 5/9 at the beginning of section 5.6. These equations will give you the magnitudes of the tangental and normal components of relative accelerations. Since the problem only asks for the magnitude of the acceleration at D, this is a good approach to take.
Whoops. I misread the hints. Disregard my "help."
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