How Do You Calculate the Rotational Inertia of a Wheel?

[Mr. Sinister]

Homework Statement

A force of 21.09 N is applied tangentially to a wheel of radius 0.340 m and gives rise to an angular acceleration of 1.20 rad/s ^2. Calculate the rotational inertia of the wheel.

a) 7.46 kg . m2
b) 4.98 kg . m2
c) 8.96 kg . m2
d) 5.97 kg . m2

Homework Equations

Do I use some type of inertia equation?

The Attempt at a Solution

My problem is I seem to not know where to start?

 

[hage567]

The force is creating a torque on the disk. Can you relate torque to force, and torque to angular acceleration? There are two equations you need to use and put together to find the moment of inertia.

 

[Mr. Sinister]

I found an equation that states the total torque equals the moment of inertia of the body. Does this help me somehow?

 

[hage567]

Well I think you're missing a bit. Does that equation look like this

$$\tau=I\alpha$$ where $$\alpha$$ is angular acceleration.

Yes, you need this.

Now you need to find a way to relate torque to force.

 

[Mr. Sinister]

Ok, cool, I found radius times force times sin theta which equals torque.

 

[Mr. Sinister]

It seems I have the radius and force for the equation but I don't have Sin. Is the wheel considered 360 degrees?

 

[hage567]

You don't have to consider the angle here because the force is applied tangentially to the rim of the wheel (so sin90 = 1), and not at an angle.

 

[Mr. Sinister]

Ok, so for Torque I have 7.17. In the equation that you gave me I do not have inertia but I do have angular acceleration. How do solve for inertia and tie these two ends together?

 

[hage567]

In the equation I gave you in post #4, I is the moment of inertia. You know what the torque is now, so you can find I.

 

[Mr. Sinister]

Great, Thank You very much ! You are extremely helpful! I know you helped me last time too. I wish I could figure out how to tackle these problems from the get go. How do I know which equations to use?

 

[hage567]

Well, you need to know the physical concepts so you know what's going on in the problem and can pick the right course of action. Knowing what the equations mean is also important. Drawing a diagram and listing everything you know and everything you need helps to keep track of things. Other than that, just practice. The more problems you do the easier it becomes for you to see how to solve them.

 

[Mr. Sinister]

Nice, thanks. I have a test next week and I am trying to figure out some of these problems. I will probably post another one here.