Spinning Bike Wheel Direction: Answer 2

[bmoore509]

1. Homework Statement
{Number 5 on attachment. It has picture.}

When a spinning bike wheel is placed hor-
izontally, hung from a pivot at one end, the
axis of rotation of the wheel will swing in a
horizontal circle.


In which direction does it turn (as viewed
from above)?
1. downward
2. horizontally, CCW
3. upward
4. horizontally, CW


2. Homework Equations
Any? I'm unsure.


3. The Attempt at a Solution
I was thinking that it was downward, but I'm not sure how to prove my answer. (We're supposed to show work.) Any help?

 

[tiny-tim]

hi bmoore509!

just do it logically …

what is the external force?

so what is the direction of the external torque?

so what will it do to the angular momentum (and what does that mean for the position of the axle)?

 

[bmoore509]

The external force would be gravity, right? That's what's leading me to believe it's going downward but I know I could be wrong.

 

[tiny-tim]

hi bmoore509!

(just got up :zzz: …)

The external force would be gravity, right? That's what's leading me to believe it's going downward but I know I could be wrong.

yes, the external force is downward …

so in which direction is the torque ? ​

 

[bmoore509]

This is when you use the right hand rule, correct? Because it's T= r X F?

But the image shows T pointing up. So do I just use that?

 

[tiny-tim]

hi bmoore509!

But the image shows T pointing up. So do I just use that?

I don't know what that T is, perhaps it's something to do with tension in the supporting cable.

but it isn't the torque … torque is always illustrated with a little round arrow, not a straight one

(and we usually write τ for torque, not T )

This is when you use the right hand rule, correct? Because it's T= r X F?

Yup!

… so which direction is the torque ?

 

[bmoore509]

I'm not 100% sure which direction r is. But wouldn't it be the direction of the arrow?

So Torque would point out towards us, right?

(Sorry, physics is not my best subject)

 

[tiny-tim]

I'm not 100% sure which direction r is.

the important question is: which point are we going to decide to take torque (and angular momentum) about?

we want to eliminate unknown forces, and the force at the pivot is unknown, so that's the point to choose!

(plus, of course, it's the obvious point to choose anyway! )

that means that, for torque and for angular momentum, r will be measured from the pivot

 

[bmoore509]

So Torque would actually be pointing away then. If I'm picturing everything correctly.

 

[tiny-tim]

So Torque would actually be pointing away then. If I'm picturing everything correctly.

uhh? everything points away …

which away do you mean? ​

 

[bmoore509]

Oh my. Haha. I meant pointing away from us.

 

[tiny-tim]

i'm still not clear

which direction, relative to the axle and to the vertical?

 

[bmoore509]

Well, my original thought was that it's the opposite side of the axle. Like the direct opposite.

 

[tiny-tim]

Well, my original thought was that it's the opposite side of the axle. Like the direct opposite.

but r is along the axle …

how can r x F be opposite it? ​

 

[bmoore509]

So then it'd be pointed to the left of the axle.

Ugh. I'm no good at this.

 

[tiny-tim]

yes, it's horizontal and tangential (but isn't it to the right?)

ok, if that's the torque (about the pivot), then what will it do to the angular momentum of the wheel (which is pointing along the axle)?

 

[bmoore509]

I'm having a total brain freeze. The other formula for torque is what?

 

[tiny-tim]

τ = dL/dt …

torque = rate of change of angular momentum

 

[bmoore509]

So if that's the rate of change of the angular momentum, how does that tell us the direction of the angular momentum?

 

[tiny-tim]

get some sleep! :zzz:

 

[bmoore509]

http://upload.wikimedia.org/wikipedia/commons/0/09/Torque_animation.gif

So I looked at that trying to understand. (Just want you to know where I get my logic from. Haha) So momentum is the same direction as Torque but the angular momentum, you can do sort of the right hand rule. I think I remember that from class! You point your thumb the direction of Torque and the way your fingers curl is the direction of the angular momentum.

So was I correct in seeing it downwards then? Because if I point my thumb horizontally to the right, I get my fingers curling down.

 

[tiny-tim]

http://upload.wikimedia.org/wikipedia/commons/0/09/Torque_animation.gif

that animation doesn't really help …

the ball in the animation doesn't do anything, unlike the wheel in your question which is itself rotating …

the wheel has an additional angular momentum (like the Earth has angular momentum from going round the Sun and angular momentum from spinning on its own axis)

So momentum is the same direction as Torque

i'm not even sure what this means, but anyway it's rubbish, forget it

but the angular momentum, you can do sort of the right hand rule. I think I remember that from class! You point your thumb the direction of Torque and the way your fingers curl is the direction of the angular momentum.

τ = r x F, so you point the thumb along the first one (r), and your index finger along the second one (F), and then your other fingers give you the cross-product, τ.

So was I correct in seeing it downwards then? Because if I point my thumb horizontally to the right, I get my fingers curling down.

where are you pointing your index finger?

 

[bmoore509]

Sorry. I'm just having a really hard time visualizing this.

I'm really not sure what I'm supposed to be doing here.

 

[tiny-tim]

Sorry. I'm just having a really hard time visualizing this.

I'm really not sure what I'm supposed to be doing here.

your angular momentum L has two components

one is the "orbital" angular momentum, which is constant, so you can ignore that

the other is the "internal" angular momentum L_w of the wheel on its own axle, which is constant in magnitude, but is along the direction of r

that is changing: draw L_w at two different times (close together), to see the direction of dL_w/dt …

you need that to be the same direction as τ ​

 

[bmoore509]

But how do I figure out how to draw L_w?

 

[tiny-tim]

But how do I figure out how to draw L_w?

uhh?

the other is the "internal" angular momentum L_w of the wheel on its own axle, which is constant in magnitude, but is along the direction of r