Help Flywheel Rotational Dynamics

In summary, the conversation discusses finding the time it takes for a flywheel with known moment of inertia and diameter, and a tangential friction force of 1000N, to come to rest. The equations used are Tau = I alpha and omega = omega_0 + alpha*t, with the result being 0.2 seconds, which can be expressed as 0.0033 minutes. However, the answer seems uncertain due to the unknown mass and lack of information on the shape of the flywheel's surface.
  • #1
Kalus
37
0

Homework Statement


You have a flywheel rotating at 1000rpm. It has a moment of inertia of 0.5 Kgm^2 and a diameter of 0.5m.

It is unclear if you know the mass. You know the moment of inertia, which is calculated using mass, but whilst the flywheel is circular I'm not sure that the surface area is that of a circle (as it may have ridges or something cut into it)

A tangential friction force is then applied to the rim of the flywheel (in the opposite direction of rotation to the flywheel), the force is 1000N.

Find the time it takes in minutes for the flywheel to come to rest.


Homework Equations



image006.gif


Not sure if any other equations are needed...

I've tried a few attempts, but i don't want to list them incase they influence anyones thinking

Many thanks, Kalus.
 

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  • #2
You have, in that array of equations that you splatter up there,

Tau = I alpha
and if you think about it, the torque will be Tau = f*r = friction force * radius, both known

Thus alpha = (f*r)/I where everything on the right is known.
This is motion under a constant (angular) acceleration. Can you take it from there?
 
  • #3
As you suggested, i did that previously...

if you plugin the values:

alpha = (f*r)/I

alpha = (1000*0.25)/0.5

which means alpha= 500

Then if you use the equation omega = omega_0 + alpha*t from down below...

you know omega (the rotational velocity, which is 1000rpm * 2pi /60)

but when you plug the numbers in you get 0.2 seconds... it doesn't seem right at all, especially given the question asks for the time in minutes...
 
  • #4
It is entirely possible to express 0.2 seconds in minutes.

The way the problem was expressed, it indicated that the friction force was 1000 N. If the intent was that the normal force was 1000 N, then there needs to be included a coefficient of friction that will multiply this value to give a somewhat lower actual friction force and hence a lower angular acceleration. This will take longer to slow down. But, with what is given, this is what we get.
 
  • #5
I know it is of course possible to express it in minutes,but i thought that an answer of 0.0033 minutes seemed a bit off, especially as they asked it for the time in minutes (leading me to expect +60s times). Unfortunatey because I've never seen a flywheel of this size and don't know the mass, i have no idea if the answer seem sensible.

The way the question is worded the force is tangetial, and no coefficeient of friction is given.

Can you think of any other possible approaches or where this could be going wrong?

Many thanks for your help Dr. D

Kalus
 

What is rotational dynamics?

Rotational dynamics is the study of the motion and forces involved in rotating objects. It involves concepts such as torque, angular velocity, and moment of inertia.

What is a flywheel and how does it work?

A flywheel is a mechanical device that stores rotational energy. It works by converting linear motion into rotational motion, and vice versa. It can also maintain a constant rotational speed due to its inertia.

How does rotational dynamics apply to flywheels?

Rotational dynamics is crucial in understanding the behavior of flywheels. It helps determine the amount of torque required to accelerate or decelerate a flywheel, as well as its angular velocity and stability.

What factors affect the rotational dynamics of a flywheel?

The rotational dynamics of a flywheel can be influenced by its mass, distribution of mass, moment of inertia, and external forces such as friction. The shape and size of the flywheel also play a role.

What are some real-life applications of flywheel rotational dynamics?

Flywheels have various practical uses, such as in engines and energy storage systems. They are also used in gyroscope stabilization and mechanical watches. In industries, they can be used to store excess energy and release it when needed, reducing energy costs.

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