Angular Acceleration with a Change in Rotational Axis

[Ignoramus]

Homework Statement

A wheel spins at 45rpm with its spin axis vertical. After spinning 15 sec, it is spinning at 60rpm with its axis horizontal. Find its average angular acceleration and the angle the avg acceleration vector makes with the horizontal.

Homework Equations

Sorry, I can't really do the latex stuff, or whatever it's called.

Avg Angular Accel = Delta Omega over Delta t

The Attempt at a Solution

They're really easy numbers... I just converted rpms into rads/s for both so I got

3pi/2 rad/s for 45rpm and 2pi rad/s for 60rpm

Then I did pi/2 divided by 15 seconds for pi/30 rad/s² And of course my answer doesn't match up. I also said that the vector would be parallel to the horizontal, since it should be parallel with the angular velocity vector. The only main variable in the problem is the change of axis of rotation. Would that affect the number and angle I'm supposed to get? How do I figure that out if it does...? I thought this was a simple problem...but maybe not

Please and thanks.

 

[Ignoramus]

Uhm...any help please?

 

[Ignoramus]

I don't know if I'm allowed to bump my threads, but nobody has helped :\

 

[ideasrule]

Angular velocity is a vector quantity, so you can't just subtract the magnitudes of the vectors and divide the result by time. Instead, you need to draw a vector diagram, identify the vector representing the change in angular velocity, and calculate its direction & magnitude. To start you off, the angular velocity vector points upwards if something's rotating counterclockwise and downwards if it's rotating clockwise.

 

[Ignoramus]

But how would I represent that with a vector diagram? The only thing that might would affect it would be the change in rotational axis going from vertical to horizontal...but that's not really a vector. That's why I don't really know where to go with this problem because when the rotation is with a vertical axis, the angular acceleration is either up or down. When it's horizontal, the angular acceleration is parallel with the axes either to the left or right. It's like the problem is giving two separate and distinct situations.

 

[ideasrule]

But how would I represent that with a vector diagram? The only thing that might would affect it would be the change in rotational axis going from vertical to horizontal...but that's not really a vector. That's why I don't really know where to go with this problem because when the rotation is with a vertical axis, the angular acceleration is either up or down. When it's horizontal, the angular acceleration is parallel with the axes either to the left or right. It's like the problem is giving two separate and distinct situations.

Imagine if the two vectors represented not angular velocity, but position. So Alice walked upwards 3pi/2 m while Bob walked 2pi m horizontally. What's the distance between them, and in what direction does Alice think Bob is at? You find the difference in angular velocity the same way you find displacement: by finding the "distance" between the tip of first vector and the tip of the second, then finding angle you need to walk at to get from the first vector to the second.

 

[Ignoramus]

That makes a ton of sense... I think I understand what you're saying now. Thank you!