SUGGESTIONS:Before starting the problem, note that the authors did not tell us exactly where point B is on the disk. The reason for this is that the final answer is true for ANY point on the disk. The magnitude and direction of the acceleration (relative to line OB) for any point at a radial distance r from O is the same. You can see this directly from the acceleration equation. Also, the ratio of alpha x r_B/O to omega x (omega x r_B/O) (which defines the angle of theta) is independent of the value of r. Therefore you can choose any point of the disk (other than O) as point B.
- Write down the rigid body kinematics equation relating the velocities of O and A: v_A = v_O + omega x r_A/O.
- Use the known speed of A in the above equation to find the omega for the disk.
- Write down the rigid body kinematics equation relating the accelerations of O and B: a_B = a_O + alpha x r_B/O + omega x (omega x r_B/O). [As described above, choose any point that you want for B.]
- Use the known direction for the acceleration of B in the above acceleration equation along with the omega found in 2 to find alpha.
11 comments:
I am having some trouble finding the answer on this one,the value of omega im using is -8 rad/s.
Your answer for omega is correct.
If you scan your solution (or take picture of it with your cell phone) and email it to me, I will look it over and advise.
I have a few more ideas im going to try, but if im still stuck i will definetly do that, thanks
Prof k,
I figured out what I was doing incorrectly, the value .6 was the ratio, not an acceleration value, once I realized my mistake then i solved for alpha using the tangent relationship.
I was wondering if there was more than approach for solving this problem where we would not have to solve for the angular velocity first. Or is it always necessary that the angular velocity be known to determine the angular acceleration?
Is it always advantageous to use a cartesian coordinate system because of the cross-products or will it ever be useful to use polar or path coordinates?
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I was wondering if there was more than approach for solving this problem where we would not have to solve for the angular velocity first. Or is it always necessary that the angular velocity be known to determine the angular acceleration?
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The short answer is no, you need to find omega first.
The longer answer is that the acceleration of a point on this disk depends on two things: alpha and omega. As you have seen, the direction of this vector depends on the ratio of r*alpha to r*omega^2. Since this ratio is just one equation and this ratio has two unknowns, you need to have another equation. That equation here is finding the omega from the known speed at point A.
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Is it always advantageous to use a cartesian coordinate system because of the cross-products or will it ever be useful to use polar or path coordinates?
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This is a very good question. In theory, you can use any description (Cartesian, path or polar) to set up the vectors needed for this equation. In practice. Cartesian is the easiest to use in almost all cases. We will see a couple problems in the next few days where knowing the path description will help us out. In the end, however, Cartesian will still be the easiest to use.
Thanks for asking this question.
i am still unsure how to use the 0.6 ratio and the tangent, any advice?
Kyle,
Really, the biggest hint I can give you is that this the key to finding alpha.
"the ratio of alpha x r_B/O to omega x (omega x r_B/O) (which defines the angle of theta)"
-Convert this to math and solve.
Important note: we're dealing with radians.
Thanks,
Jon
Biberstine ,
thank you for the help, i did not realize it was a direct relationship, i was trying to impliment to much trig. thanks again
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