Calculating Moment of Inertia and Frictional Torque for Rotating Wheel

[nns91]

Homework Statement

1.
A wheel mounted on an axis that is not frictionless is initially at rest. A constant external torque of 50 N.m is applied to the wheel for 20s, giving the wheel an angular velocity of 600 rev/min. The external torque is then removed, and the wheel comes to rest 120 s later. Find (a) the moment of inertia of the wheel, and (b) the frictional torque, which is assumed to be constant.

2. A wagon wheel 1.0m in diameter consists of a thin rim having a mass of 8kg and six spokes each having a mass of 1.2kg. Determine the moment of intertia of the wagon wheel for rotation about its axis.

Homework Equations

$$\tau$$ = I*$$\alpha$$

The Attempt at a Solution

1. I found out the moment of inertia by subsituting 50 for $$\tau$$ and calculat the angular acceleration by change in velocity / change in time.

How do I do part b ?? I am kind lost and don't know what approach to use.

2.So how do I approach this problem ? Do the spkes matter ?? Do I need an integration here ??

 

[berkeman]

Homework Statement

1.
A wheel mounted on an axis that is not frictionless is initially at rest. A constant external torque of 50 N.m is applied to the wheel for 20s, giving the wheel an angular velocity of 600 rev/min. The external torque is then removed, and the wheel comes to rest 120 s later. Find (a) the moment of inertia of the wheel, and (b) the frictional torque, which is assumed to be constant.

2. A wagon wheel 1.0m in diameter consists of a thin rim having a mass of 8kg and six spokes each having a mass of 1.2kg. Determine the moment of intertia of the wagon wheel for rotation about its axis.

Homework Equations

$$\tau$$ = I*$$\alpha$$

The Attempt at a Solution

1. I found out the moment of inertia by subsituting 50 for $$\tau$$ and calculat the angular acceleration by change in velocity / change in time.

How do I do part b ?? I am kind lost and don't know what approach to use.

2.So how do I approach this problem ? Do the spkes matter ?? Do I need an integration here ??

Not sure your approach to (1) is correct. 50Nm is not the net accelerating torque... You should write two equations for the behavior of the wheel, and use them to solve for the two unknowns...

 

[nns91]

What are those two equations then ?

 

[berkeman]

What are those two equations then ?

You tell us. You know how the Homework Help forums work...

 

[nns91]

I guess it will base on the T=I*a (I mean T as torque and a as alpha).

I can calculate alpha so I still have T and I left.

So I know the external torque is 50 but there is friction also but I don't know friction yet.

Can you give me like a hint ??

 

[berkeman]

I guess it will base on the T=I*a (I mean T as torque and a as alpha).

I can calculate alpha so I still have T and I left.

So I know the external torque is 50 but there is friction also but I don't know friction yet.

Can you give me like a hint ??

Hint -- when the wheel is spinning up, how many torques are acting on it? When it is spinning down, how many torques are acting on it?

 

[nns91]

When it spins up, there is one at the top, when it spins down, there is one at the bottom.

Am I right ??

 

[berkeman]

When it spins up, there is one at the top, when it spins down, there is one at the bottom.

Am I right ??

That's not the way I'm reading the problem (but I could be wrong I guess). It sounds like there is axle friction (not sure why it's called axis friction) torque. Friction always retards motion, right?

 

[nns91]

yep. So Torque= 50- Friction torque right ?? However, I don't know friction torque.

 

[berkeman]

yep. So Torque= 50- Friction torque right ?? However, I don't know friction torque.

Two equations and two unknowns...

 

[nns91]

So the first one will be: 50- Friction = alpha * I ??

 

[berkeman]

So the first one will be: 50- Friction = alpha * I ??

Just write 'em both down and solve 'em.

 

[nns91]

A dumb question but what do you mean by both ??

 

[berkeman]

Two equations and two unknowns... Write down both equations and solve away.

I have to bail in a couple minutes. Think it through.

 

[nns91]

I thought I have only one equation ??

 

[berkeman]

I thought I have only one equation ??

I'm not going to hold your hand every step of the way. Go back and read all the posts in this thread, and solve the problem. Honestly, it's all there. And check your PMs in a couple minutes.