# Hamster running in a wheel

1. Aug 30, 2007

### flash

If a hamster runs in a wheel, how do I figure out the rotational velocity that the wheel achieves (after it stops accelerating)? Is it to do with the mass of the hamster or the speed at which it runs?
I'm familiar with the basic concepts of rotational motion (moment of inertia, torque etc) but unsure of where to go. Any help appreciated!

2. Aug 30, 2007

### Dick

This isn't a technical question - think! If the speed were determined by the weight of the hamster, then a dead one would work as well as a live one. Clearly, yes, it's the running speed.

3. Aug 30, 2007

### flash

Lol I guess so. But isn't it the weight force of the hamster that causes the torque? If its just the speed then how would I work out the angular velocity given the running speed of the animal?

4. Aug 30, 2007

### mgb_phys

Angular velocity is just rotations / second.
Linear spped is distance / second.
All you need to know is how much distance = 1 revolution, = 2 pi * radius

5. Aug 30, 2007

### flash

So lets say the radius was 1m and the speed of the hamster was 10m/s
1 revolution = 2pi = 6.28 metres
time for 1 rev = 2pi/10 = 0.628 seconds
angular velocity = 0.628^-1 = 1.59 rev/s = 10radians/s
Correct?

Still confused, if there was no friction wouldn't the angular velocity increase forever? If not then somewhere along the way there is no net torque?

Also if this wheel were to power a generator or turn something heavy, how would this effect the result?

Last edited: Aug 30, 2007
6. Aug 30, 2007

### mgb_phys

If there is no friction and the hamster can keep running faster and faster forever then there is no limit until the hamster starts approaching the speed of light. (the relativistic hamster problem)
The hamster does apply a torque to the wheel to move it but torque is just a force, you don't store up torque - you store angular momentum.

7. Aug 30, 2007

### Dick

10m/sec? That's a FAST hamster. Even if it is nonrelativistic.

8. Aug 30, 2007

### flash

But as long as it's applying a torque the wheel accelerates right?
It ran at 10m/s to make my life easier :)

9. Aug 30, 2007

### mgb_phys

You are thinking that if the hamster supplies a constant torque the wheel must get a constant acceleration and so get faster.
If the hamster as outside the wheel and just gave it a single constant force kick on each revolution then it would accelarate.

10. Aug 30, 2007

### flash

If it had a load on the wheel (like a generator) am I right to assume that this increases the moment of inertia? It would seem that the top speed of the wheel should be slower though?

Last edited: Aug 30, 2007
11. Aug 30, 2007

### BobG

The simple relationship between angular velocity and linear velocity is:

$$v=r \omega$$

Additionally, if the hamster can only move his legs so fast (fast enough to go 10 m/s), then eventually the hamster can do no more than spin the wheel at a constant speed. The hamster provides an initial torque that decreases as the speed increases until the hamster is moving as fast as it can go.

You might be able to calculate the speed of a hamster if you could estimate the radius of the wheel in this video (http://www.glumbert.com/media/hamsterwheel). I think the display is showing km/hr, but the speedometer is designed for a larger wheel. Supposedly, dividing by 10 gives the correct km/hr, but that's twice the speed of the hamsters in another study (http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=1769401).

10 m/s would be one fast hamster in any event!

12. Aug 30, 2007

### mgb_phys

It could be an observational bias, if there was a species of hamster capable of 10m/s would anyone have caught one to classify it?

13. Oct 17, 2008

### HPP

I recommend a scoped .17 caliber varmint rifle w/tranq dart.