How should we approach the third and fourth term of solving for alpha? I’m not sure what to put for the terms for.
You can follow the general procedure of the lecture book examples.
I have got the equations set up for the angular velocity and the angular acceleration, the problem is I am unsure how to make my answer in terms of the xyz coordinate system instead of the XYZ coordinate system and they are also not aligned at the instant, so I do not know this procedure.
Consider the angle between the Y and x & y. Since we are given theta, we can find the relation between all three of those using trig. You should be able to set up the represent x and y as components of Y. Hope that helps!
For the instant of interest, k and K are aligned. This means that the ij unit vectors are in the same plane as the IJ unit vectors.
* If you need to write I in terms of i and j, then just use vector projections that we used earlier in the course when we transformed unit vectors from one coordinate system to another (and as you did so in ME 270). You can check in Chapter 0 of the lecture book for more details on this.
* Same way for writing J in terms of i and j.
By xyz terms, do they mean by the lower case terms like how there is i j k and I J K?
Yes they are. i j k is x y z and I J K is X Y Z
Is omega_disk in the positive or negative i direction in this problem? Should we rely on the figure or the value provided in the problem when it comes to the signs?
From the figure, it is given that omega_disk points in the negative x-direction. Its angular speed is 6 rad/s.
How should we approach the third and fourth term of solving for alpha? I’m not sure what to put for the terms for.
You can follow the general procedure of the lecture book examples.
I have got the equations set up for the angular velocity and the angular acceleration, the problem is I am unsure how to make my answer in terms of the xyz coordinate system instead of the XYZ coordinate system and they are also not aligned at the instant, so I do not know this procedure.
Consider the angle between the Y and x & y. Since we are given theta, we can find the relation between all three of those using trig. You should be able to set up the represent x and y as components of Y. Hope that helps!
For the instant of interest, k and K are aligned. This means that the ij unit vectors are in the same plane as the IJ unit vectors.
* If you need to write I in terms of i and j, then just use vector projections that we used earlier in the course when we transformed unit vectors from one coordinate system to another (and as you did so in ME 270). You can check in Chapter 0 of the lecture book for more details on this.
* Same way for writing J in terms of i and j.
By xyz terms, do they mean by the lower case terms like how there is i j k and I J K?
Yes they are. i j k is x y z and I J K is X Y Z
Is omega_disk in the positive or negative i direction in this problem? Should we rely on the figure or the value provided in the problem when it comes to the signs?
From the figure, it is given that omega_disk points in the negative x-direction. Its angular speed is 6 rad/s.