How Do You Calculate Average Angular Acceleration with Axis Orientation Change?

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SUMMARY

The discussion centers on calculating average angular acceleration when a wheel transitions from spinning at 44 RPM with a vertical axis to 60 RPM with a horizontal axis over 15 seconds. The initial calculation of average angular acceleration was incorrectly derived as 0.11 rad/s² due to unit conversion errors and neglecting the vector nature of angular velocity. Properly accounting for the change in orientation and ensuring consistent units are crucial for accurate calculations.

PREREQUISITES
  • Understanding of angular velocity and angular acceleration
  • Familiarity with unit conversions, specifically from RPM to rad/s
  • Knowledge of vector quantities in physics
  • Basic principles of rotational motion
NEXT STEPS
  • Study the concept of angular acceleration in detail
  • Learn about unit conversions between RPM and rad/s
  • Explore vector addition and its application in angular motion
  • Investigate the effects of axis orientation changes on angular velocity
USEFUL FOR

Physics students, mechanical engineers, and anyone involved in rotational dynamics or angular motion calculations will benefit from this discussion.

Aseri
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A wheel is spinning at 44 with its axis vertical. After 15 , it's spinning at 60 with its axis horizontal. Find (a) the magnitude of its average angular acceleration and (b) the angle the average angular acceleration vector makes with the horizontal.

Just trying to work out what I'm doing wrong here to find the average angular acceleration.

I used angular acceleration = final velocity - initial velocity all divided by the time pasted.
(Also converted units from rpm to rad/s2 by multiplying by (2∏/60)So far my initial answer is 0.11 rad/s2 which is apparently wrong, any idea what I can be doing wrong here?
 
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Aseri said:
A wheel is spinning at 44 with its axis vertical. After 15 , it's spinning at 60 with its axis horizontal.
What are the units here?
44rmp, 15mins, 60rpm ...
44rad/s, 15s, 60rad/s ...
something else?

Reading on - perhaps it is a mixture of unit types - rpm for frequency and s for time?
It is best practice to include units in the description.

Find (a) the magnitude of its average angular acceleration and (b) the angle the average angular acceleration vector makes with the horizontal.

Just trying to work out what I'm doing wrong here to find the average angular acceleration.

I used angular acceleration = final velocity - initial velocity all divided by the time pasted.
(Also converted units from rpm to rad/s2 by multiplying by (2∏/60)

So far my initial answer is 0.11 rad/s2 which is apparently wrong, any idea what I can be doing wrong here?
Did you include the change in orientation too? Angular velocity is a vector.

If it were linear motion and I said I'd been going 44m/s north and 15 seconds later I was going 60m/s south ... would the average acceleration be (60-44)/15 ?
 

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