If you just use x as a variable in the vector for r(c/o) then x will no longer be considered when you do the cross product since omega O is in the J direction. I think.

Does anyone else sometimes decide to isolate for the velocity and acceleration of a single segment of a dependent/relative system in order to try to understand how its moving before trying to relate that the the observer? I feel like it helps me conceptually understand better, but it takes longer.

When it asks for the angular velocity of the disk, that means omega total at the disk right? Because it gives us a value called omega disk and thats kinda confusing...

You are correct. The nomenclature here is not very clear. You are asked to find the total angular velocity of the disk. omega_disk is a component of the angular velocity of the disk relative to the arm.

Consider that point C moves on a circular path of radius "b" with a constant speed of b*omega_0. Use that to determine the acceleration vector for point C.

I think there might be a mistake in the solution video around 10:30. You say k x i is -j, making the sign of r*w_d^2 positive, but isn't k x i equal to j, keeping the term negative?

If we want to relate vc to vo first, then, vb to vc. how we can find the distance between point C and point O in x direction.

If you just use x as a variable in the vector for r(c/o) then x will no longer be considered when you do the cross product since omega O is in the J direction. I think.

Does anyone else sometimes decide to isolate for the velocity and acceleration of a single segment of a dependent/relative system in order to try to understand how its moving before trying to relate that the the observer? I feel like it helps me conceptually understand better, but it takes longer.

When it asks for the angular velocity of the disk, that means omega total at the disk right? Because it gives us a value called omega disk and thats kinda confusing...

You are correct. The nomenclature here is not very clear. You are asked to find the total angular velocity of the disk. omega_disk is a component of the angular velocity of the disk relative to the arm.

In part b, the omega in the equation used to solve for the acceleration of Ac is not the same that we found in part a, correct?

Consider that point C moves on a circular path of radius "b" with a constant speed of b*omega_0. Use that to determine the acceleration vector for point C.

I think there might be a mistake in the solution video around 10:30. You say k x i is -j, making the sign of r*w_d^2 positive, but isn't k x i equal to j, keeping the term negative?