For solving this Problem 7/19, would it be better to use the method similar to the example on p.61 of the notes, or should we be using the velocity and acceleration equations that we have been using thus far? Thank you.
-Dale Szul-
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4 comments:
Both, actually.
1. Attach observer/xyz to disk. XYZ is a set of FIXED axes.
2. Write down the omega vector for the disk: omega = omega1*J - omega2*k (see figure for terminology).
3. Use the moving reference frame velocity equation to relate the velocities of points O and C: v_C = v_O + (v_C/O)_rel + omega x r_C/O. Since both C and O are points with zero velocity and since the observer on the disk sees C as being fixed, all terms EXCEPT the last term in the above equation is zero. This very simple equation will then give you the relationship between omega_1 and omega_2 (and hence between omega_1_dot and omega_2_dot).
4. Differentiate the angular velocity equation in 2. above to find the angular acceleration of the disk.
Note: Please do NOT find the space cone, as asked in the problem (we are not covering that this semester).
when i cross omega, which i have as (-omega1*J-omega2*k) with R*k, then i get 0=-omega1*I-omega2*0 or omega1 = 0 and i dont know how that helps, i guess i just dont know what im doing wrong.
can't you just find omega by adding omega_1(fixed axis) and omega_2(rotating axis), then take the derivative, then ultimately end up with the same result as on p.61 of the notes, and plug in the numbers? I did that and got the answer in the book. I just found omega_2 by taking the ratio of the circumfrences of the circular arc and the disk and multiplying them by 2pi/tau. Did I just stumble upon the right answer or is that correct?
-Adam Watson
--Kyle--
You need to check your r_C/O vector: this vector needs to go from O to C. Your vector goes only from O to the center of the disk.
--Adam--
Your method is fine. When you" found omega_2 by taking the ratio of ..." you are doing exactly the same thing with instant centers as the vector equation with which Kyle is working.
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