Angular Acceleration Problem

In summary, the conversation is about finding the total linear acceleration using the angular acceleration, angular velocity, and radius of curvature. The person initially thought they could use the second derivative to find the angular acceleration, but it did not give the correct answer. Another person suggests considering the centripetal acceleration and reminds them to find the vector sum of both components. The conversation ends with the person understanding and thanking the other for their help.
  • #1
Garen
28
0

Homework Statement


35klkrc.jpg




The Attempt at a Solution


I thought I could take the second derivative and get the angular acceleration from which I could use
16b8cfa99b346f088634c4ef6c1150d0.png
where ω is the angular velocity,
023d6d214986966742c67e809c7ee176.png
is the linear tangential acceleration, and r is the radius of curvature. But for some reason, it didn't give me the right answer, anyone know where I went wrong?
 
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  • #2
Hi Garen,

Garen said:

Homework Statement


35klkrc.jpg




The Attempt at a Solution


I thought I could take the second derivative and get the angular acceleration from which I could use
16b8cfa99b346f088634c4ef6c1150d0.png
where ω is the angular velocity,
023d6d214986966742c67e809c7ee176.png
is the linear tangential acceleration, and r is the radius of curvature. But for some reason, it didn't give me the right answer, anyone know where I went wrong?

Are you saying that you put in the tangential acceleration as your answer? If so, remember that they are asking for the total linear acceleration, and there is more to the total acceleration than just the tangential part.
 
  • #3
aaaah thank you so much. i was totally stalking this post and you replied to it in a MOMENT OF PARADISE!
 
  • #4
alphysicist said:
Hi Garen,



Are you saying that you put in the tangential acceleration as your answer? If so, remember that they are asking for the total linear acceleration, and there is more to the total acceleration than just the tangential part.

Oh, I thought that total linear acceleration was only the tangential acceleration...Would I have to include centripetal acceleration? If so, how?
 
  • #5
Garen said:
Oh, I thought that total linear acceleration was only the tangential acceleration...Would I have to include centripetal acceleration? If so, how?

What is the formula for centripetal acceleration? (And remember that you have already found the angular velocity!)

Once you have found both components (the tangential and centripetal), the total is just the vector sum.
 
  • #6
alphysicist said:
What is the formula for centripetal acceleration? (And remember that you have already found the angular velocity!)

Once you have found both components (the tangential and centripetal), the total is just the vector sum.

I got it! Thanks a lot for your help.
 
  • #7
Garen said:
I got it! Thanks a lot for your help.

Sure, glad to help!
 

1. What is angular acceleration?

Angular acceleration is the rate of change of angular velocity. It measures how quickly an object's angular velocity is changing over time.

2. How is angular acceleration calculated?

Angular acceleration is calculated by dividing the change in angular velocity by the change in time. The formula for angular acceleration is α = Δω / Δt, where α is angular acceleration, Δω is the change in angular velocity, and Δt is the change in time.

3. What is the difference between angular acceleration and linear acceleration?

Angular acceleration refers to the change in an object's rotational speed, while linear acceleration refers to the change in an object's linear speed. Angular acceleration is measured in radians per second squared, while linear acceleration is measured in meters per second squared.

4. How does angular acceleration relate to torque?

Angular acceleration is directly proportional to the torque applied to an object. This means that the greater the torque, the greater the angular acceleration. The relationship between torque and angular acceleration is described by the equation α = τ / I, where α is angular acceleration, τ is torque, and I is moment of inertia.

5. How can angular acceleration be applied in real-world situations?

Angular acceleration can be used to study the motion of objects that rotate, such as planets, gears, and wheels. It is also important in understanding the movement of objects in sports, such as the spin on a baseball or the rotation of a figure skater. Additionally, it is a crucial concept in the design and operation of machines and vehicles that involve rotational motion, such as cars and airplanes.

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