Changing angular acceleration of a shaft

In summary, the conversation is about finding the angular speed of a shaft at 3 seconds given its initial angular velocity and angular acceleration. The speaker is stuck on how to take the derivative of the angular acceleration in order to calculate small sections of a/t. They are advised to integrate the function and find the velocity, taking into account the constant of integration. They are also recommended to find a and b and suggested to look for a calculus website that focuses on physics applications for further help.
  • #1
jmf322
18
0
Hello, I'm stuck on this problem and I think its because I am lacking the calculus to get the correct answer.

A shaft is turning at 65 rad/s at time = 0. After, its angular acceleration is given by:

a= -10.0 rad/s^2 - 5.00t rad/s^3 where t is the elapsed time.

Find its angular speed at 3 seconds.

Now where I am stuck is I can find its acceleration at 3 seconds, but I believe I need to take the deritive of something in order to calculate the small sections of a/t. Am I on the right track? Any good links to explain how to take the deriitive of a angular acceleration? Thanks!
 
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  • #2
if: a=-10-5t

then the velocity is the integral of this function, so, integrate this to find the velocity,

but remember your constant of integration! so you will have a function something like this,

V= - at - 1/2 bt^2 + C C is a constant of integration,

you already know what this value SHOULD be though, becuase they told you the speed at time 0 is 65. So you have to solve such that 65= - at - 1/2 bt^2 + C ,when time t is zero, this will tell you what C is.

Now you have your general equation, and you just plug in 3 for time to get your angular speed. But ill leave finding a and b to you. it should look similar though.
 
  • #3
thanks for the help! Do you or anyone else know of any good calclus with physics applications help site? I understand the Physics in my class, but i struggle with the calculus and calculus web sites are very broad. Thanks again!
 

What is angular acceleration?

Angular acceleration, also known as rotational acceleration, is the rate of change of angular velocity. It is a measure of how quickly the rotational speed of an object is changing.

Why is it important to change angular acceleration of a shaft?

Changing the angular acceleration of a shaft can impact the overall speed and movement of a rotating object. It can also affect the forces acting on the object and its stability.

How can the angular acceleration of a shaft be changed?

The angular acceleration of a shaft can be changed by applying a torque, which is a force that causes rotation. This can be done by using a motor, gears, or other mechanical components.

What factors can affect the angular acceleration of a shaft?

The angular acceleration of a shaft can be affected by the mass and distribution of the object being rotated, the amount of torque applied, and any external forces or friction present.

What are some real-world applications of changing angular acceleration of a shaft?

Changing angular acceleration of a shaft is important in many fields, including engineering, physics, and robotics. It is used in machines such as engines, turbines, and motors to control the speed and movement of rotating parts.

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