Rotational kinetic energy of a fly wheel.

AI Thread Summary
The discussion focuses on calculating the rotational kinetic energy of a flywheel with a moment of inertia of 20 kg m² under a constant torque of 40 N m applied for 3 seconds. The key equations for rotational motion, including the relationship between torque, moment of inertia, and angular acceleration, are highlighted. The user initially struggles to find the angular velocity without knowing the radius of the wheel, but is reminded that the moment of inertia serves as the rotational equivalent of mass. By applying the equation T = Iα, the user can determine angular acceleration and subsequently calculate angular velocity. This understanding allows for the eventual calculation of rotational kinetic energy.
leoflindall
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Homework Statement



The moment of inertia of a fly wheel about it's axis is 20 kg m2. A constant torque of 40 N m is applied to the initially stationary fly wheel. Find it's rotational KE after 3 seconds assuming there is no friction in the system?


Homework Equations



KE=\frac{1}{2}I\omega2
I=mr2
a=r\omega2
\tau=Fr , where \tau = torque.



The Attempt at a Solution



I know I have to work out the angular frequency. Knowing the torque applied to the wheel for a given time I should be able to work out the speed after 3 seconds, but I don't know the radius of the wheel. so I think I need to work out the angular velocity and radius, and then I can work out KE. But I can't see how to do this?

Can anyone give me any advice?
 
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Consider an analogous linear problem: A object of mass M = 20 kg is on a frictionless surface. A constant force of 40 N is applied to the initially stationary mass. Find its kinetic energy after 3 seconds.

What would your procedure be?
 
Use Newton's second law to work out the acceleration, and then the speed and then use 1/2 m v2 for the energy.

I was looking to do something similar, but I don't have the mass of the fly wheel to determine the acceleration, nor the radius to determine the acceratory force from the torque. Unless I have missed something - I don't do a lot of mechanics!

I know I'm missing something simple here!
 
leoflindall said:
I know I'm missing something simple here!

Yes, the moment of inertia is the analog of mass for rotational motion. Torque is analogous to force. Angular velocity is analogous to velocity.
 
You're missing a key equation. The applied torque is proportional to the angular acceleration. T = I a where T is the torque, I is the moment of inertia, and a is the angular acceleration. If you know a and you know how long it is applied, can you find the angular velocity?
 
I knew I was missing something, with that equation it's easy.

Thank you

Leo
 

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