Momentum and Impulse for a flywheel

[richiecky]

Hey. Just wondering if I could get a little help with this quest please.

A flywheel has a moment of inertia of 854kgm^s, and is allowed to come to rest from and angular velocity of 450rpm. Knowing that kinetic friction produces a resisting moment of magnitude 14Nm, determine the time required for the flywheel to come to rest.

well, i know that 450x(2pi/60) = 47.12 rad/min = 0.785rad/sec
so 0.785 is the intial angular velocity..

but am not sure where to go from here.
Could someone point me in the right direction please?
Thanks

 

[rl.bhat]

Moment of inertia of the flywheel and torque on it is given. From thewse values find the angular retardation alpha, which is equal = torque/I. Then using kinematics find the time.

 

[ogb p]

Sure, I'd be happy to help. To determine the time required for the flywheel to come to rest, we can use the equations for momentum and impulse. Momentum is defined as the product of mass and velocity, while impulse is the product of force and time. In this case, we can use the equation for angular momentum, which is the product of moment of inertia and angular velocity.

So, the initial angular momentum of the flywheel can be calculated as:

L = Iω = (854kgm^s)(0.785rad/sec) = 670.49 kgm^s^2

Next, we can use the equation for impulse to calculate the force acting on the flywheel. We know that the resisting moment produced by kinetic friction is 14Nm, and the flywheel has a radius of 1 meter. So, the force acting on the flywheel can be calculated as:

F = M/r = 14Nm/1m = 14N

Now, we can use the equation for impulse to calculate the time required for the flywheel to come to rest:

I = Ft = change in momentum

Rearranging for time, we get:

t = I/F = 670.49 kgm^s^2 / 14N = 47.89 seconds

Therefore, it will take approximately 47.89 seconds for the flywheel to come to rest. I hope this helps and good luck with your quest!