Angular Acceleration with a Change in Rotational Axis

In summary, the wheel is spinning at 45rpm and 60rpm, respectively, with an average angular acceleration of 3pi/2 rad/s and 2pi rad/s. The wheel is rotating with its spin axis vertical at first, but then it rotates to horizontal and the average angular acceleration vector points parallel to the horizontal.
  • #1
Ignoramus
18
0

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.
 
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  • #2
Uhm...any help please?
 
  • #3
I don't know if I'm allowed to bump my threads, but nobody has helped :\
 
  • #4
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.
 
  • #5
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.
 
  • #6
Ignoramus said:
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.
 
  • #7
That makes a ton of sense... I think I understand what you're saying now. Thank you!
 

What is angular acceleration with a change in rotational axis?

Angular acceleration with a change in rotational axis refers to the change in the rate of rotation of an object around a certain axis. It is a measure of how quickly the angular velocity of an object is changing as it rotates around a different axis.

How is angular acceleration with a change in rotational axis calculated?

Angular acceleration with a change in rotational axis can be calculated using the formula α = (ω2 - ω1) / (t2 - t1), where α is the angular acceleration, ω2 and ω1 are the final and initial angular velocities, and t2 and t1 are the final and initial times.

What factors affect angular acceleration with a change in rotational axis?

The main factors that affect angular acceleration with a change in rotational axis are the mass and distribution of mass of the rotating object, the applied torque, and any external forces acting on the object.

What is the difference between angular acceleration and linear acceleration?

Angular acceleration refers to the change in the rate of rotation of an object, while linear acceleration refers to the change in the rate of an object's linear motion. Angular acceleration is measured in radians per second squared, while linear acceleration is measured in meters per second squared.

How is angular acceleration with a change in rotational axis used in real life?

Angular acceleration with a change in rotational axis is important in many real-life applications, such as in the design of vehicles and machines that involve rotating parts. It is also used in sports, such as figure skating and gymnastics, to measure the rate of rotation of the body around a certain axis.

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