Angular Momentum of a flywheel problem

In summary, the conversation is discussing the calculation of average torque and angular displacement for a flywheel with a given rotational inertia and change in angular momentum over a period of time. After discussing the equations and approach, it is determined that the angular displacement can be found by using the kinematics equation and solving for it with the known angular acceleration and time. The importance lies in understanding the correct approach rather than focusing on the answers.
  • #1
Seraph404
64
0

Homework Statement



The angular momentum of a flywheel having a rotational inertia of 0.140 kg m[tex]^{2}[/tex] about its central axis decreases from 3.00 to 0.800 kg m[tex]^{2}[/tex]/s in 1.50 s. a) What is the magnitude of the average torque acting on the flywheel about its central axis during this period? b) Assuming a constant angular acceleration, through what angle does the flywheel turn?


Homework Equations



[tex]\tau[/tex] = I[tex]\alpha[/tex] ?


The Attempt at a Solution



a) Part a is easy. Torque equals final momentum minus initial momentum over the time. The answer is -1.47 N

b) Part b is what I need help with. As a hint, what equations should I look at or try to combine?
 
Last edited:
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  • #2
Find the angular acceleration, then use kinematics to find the angle.
 
  • #3
Well, I thought of that, but then how do I find angular velocity?
 
  • #4
Seraph404 said:
Well, I thought of that, but then how do I find angular velocity?
Using kinematics as Doc Al said. You know that,

[tex]\alpha = \frac{d^2\theta}{dt} = \frac{d\omega}{dt}[/tex]

Can you take the next step?
 
  • #5
Uh.. I'm still not getting 20.4 rad, for some reason.
 
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  • #6
Seraph404 said:
Uh.. I'm still not getting 20.4 rad, for some reason.
Perhaps if you showed us your working we could help you out.
 
  • #7
Answers are not important if you know the correct approach.

I hope my great colleagues above would agree.

Now for the help part..

Torque is the rate of change of angular momentum.
Next, torque= M*I * alpha
alpha=omega/t or omega= alpha*t
next, omega * time= angular displacement.
finally... angular displcement is what you want .rest is easy.
 
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Related to Angular Momentum of a flywheel problem

1. What is Angular Momentum of a flywheel?

Angular momentum of a flywheel is a measure of its rotational motion, and is calculated by multiplying its moment of inertia by its angular velocity. It is a vector quantity, meaning it has both magnitude and direction.

2. How is Angular Momentum of a flywheel different from Linear Momentum?

Angular momentum is a measure of rotational motion, while linear momentum is a measure of linear motion. Angular momentum takes into account the moment of inertia and angular velocity, while linear momentum takes into account mass and linear velocity.

3. What factors affect the Angular Momentum of a flywheel?

The Angular Momentum of a flywheel is affected by its moment of inertia, which is determined by the distribution of mass around the axis of rotation, and its angular velocity, which is the rate at which it rotates.

4. How is Angular Momentum of a flywheel conserved?

According to the Law of Conservation of Angular Momentum, the total angular momentum of a system remains constant unless acted upon by an external torque. This means that the Angular Momentum of a flywheel will remain constant unless there is an external force or torque acting on it.

5. How is the Angular Momentum of a flywheel used in real-life applications?

The concept of Angular Momentum of a flywheel is used in various real-life applications, such as gyroscopes in navigation systems, flywheels in energy storage systems, and spinning tops in toys. It is also used in the study of rotational motion and mechanics in physics.

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