Calculating Angular Acceleration: A Flywheel Question Explained

[janiexo]

"A flywheel 0.600 m in diameter pivots on a horizontal axis. A rope is wrapped around the outside of the flywheel, and a steady pull of 40.0 N is exerted on the rope. The flywheel starts from rest, and 5.00 m of rope are unwound in 2.00 s.
1. What is the angular acceleration of the flywheel?"

I'm just confused with this question because I'm wondering whether they want the average angular acceleration, or the angular acceleration at the beginning or at the end.

I tried to solve it by saying that angular velocity = velocity/radius where the velocity is equal to d/t (5/2) and radius is 0.3, then used angular acceleration = angular velocity/time where time = 2 and got an answer of 25/6 but it was wrong. I'm probably all over the place but I'm new to these angular concepts so any help would be appreciated

 

[OlderDan]

"A flywheel 0.600 m in diameter pivots on a horizontal axis. A rope is wrapped around the outside of the flywheel, and a steady pull of 40.0 N is exerted on the rope. The flywheel starts from rest, and 5.00 m of rope are unwound in 2.00 s.
1. What is the angular acceleration of the flywheel?"

I'm just confused with this question because I'm wondering whether they want the average angular acceleration, or the angular acceleration at the beginning or at the end.

I tried to solve it by saying that angular velocity = velocity/radius where the velocity is equal to d/t (5/2) and radius is 0.3, then used angular acceleration = angular velocity/time where time = 2 and got an answer of 25/6 but it was wrong. I'm probably all over the place but I'm new to these angular concepts so any help would be appreciated

Your problem requires understanding of the concepts of moment of inertia and torque. The angular acceleration in the problem is constant because the force is constant. The angular velocity will be constantly changing. You have the average angular velocity, from which you can find the change in angular velocity from which you can find the constant angular acceleration.

 

[janiexo]

So do I have to find the moment of Inertia of the wheel? How can I do that without knowing its mass?

 

[janiexo]

Never mind, I found another topic on the board with a similar problem

 

[OlderDan]

So do I have to find the moment of Inertia of the wheel? How can I do that without knowing its mass?

Just to wrap this up: In this problem you do not have to calculate the moment of inertia. You just need to understand that torque and angular acceleration are proportional. (We call that ratio the moment of inertia.) Because they are proportional, and because the torque is generated by a force that in this problem is a constant, the torque is constant and consequently the angular acceleration is constant. So your original question about "which aceleration" to use is answered by the fact that they are all the same. The information given in the problem allows you to compute the average angular velocity, which for constant angular acceleration is half-way between the initial angular velocity and the final angular velocity. From that you can find the change in angular velocity during the time period, and from that you can find the angular acceleration.

 

[sudhiraggarwa]

why is time period of flywheel infinity at it's center of gravity?