Angular acceleration from change in angular velocity and angle

In summary, calculating angular acceleration can be accomplished by using the formula α=ω(θ)*Δω/Δθ, where ω is angular velocity and θ is angle. This formula holds true for any angular acceleration, even if it is not constant. However, it only works for 2-D objects as 3-D objects have a more complex formula for calculating angular acceleration.
  • #1
natasha13100
58
0
Is there a way to calculate angular acceleration from the change in angular velocity and the change in the angle without considering time? How would you accomplish this?
 
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  • #2
##\alpha = \frac{\mathrm{d} \omega}{\mathrm{d} t} = \omega\frac{\mathrm{d} \omega}{\mathrm{d} \theta}## so if you know ##\omega(\theta)## you don't need to consider time.
 
  • #3
Does this work even if angular acceleration is not constant?
 
  • #4
Yes certainly; the above is true for any angular acceleration whatsoever. All you need to know is ##\omega## as a function of ##\theta##.
 
  • #5
So α=ω(θ)*Δω/Δθ?
 
  • #6
natasha13100 said:
Does this work even if angular acceleration is not constant?
It doesn't even work if angular acceleration is constant, at least not in three dimensional space (or higher).
 
  • #7
I think the OP is just talking about the angular acceleration ##\alpha = \frac{\Delta \omega}{\Delta t}## for "pancake objects" constrained to lie on a plane, in which case the above is just a consequence of the chain rule.
 
  • #8
Okay so this only works with 2-D objects.
 

1. What is angular acceleration?

Angular acceleration is the rate of change of angular velocity with respect to time. It is a measure of how quickly an object's angular velocity is changing.

2. How is angular acceleration related to change in angular velocity?

Angular acceleration is directly proportional to the change in angular velocity. This means that the greater the change in angular velocity, the greater the angular acceleration.

3. What is the formula for calculating angular acceleration?

The formula for calculating angular acceleration is: α = (ω2 - ω1) / t, where α is the angular acceleration, ω2 is the final angular velocity, ω1 is the initial angular velocity, and t is the time interval.

4. Can angular acceleration be negative?

Yes, angular acceleration can be negative. This indicates that the object is slowing down or moving in the opposite direction of its original rotation.

5. How is angular acceleration different from linear acceleration?

Angular acceleration measures the rate of change of angular velocity, while linear acceleration measures the rate of change of linear velocity. In other words, angular acceleration is related to rotational motion, while linear acceleration is related to straight-line motion.

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