# B A stick in space

1. Dec 22, 2017

### Erunanethiel

Let's say I have a 10 cm long stick in space.

If I want it's right side to rotate as much as possible (even go backwards) by pushing on it's left end, where would the ideal position of the center of mass of the stick be?

Would it be the middle, or closer to the right or left? And by how many centimeters?

2. Dec 22, 2017

### kuruman

The motion of the stick is governed by the laws of conservation of angular and linear momentum.. If the stick is uniform, the center of mass of the stick is at 5 cm from the ends, at the midpoint. There is no ideal position for it, that's where it is. If you give the stick a kick, in general it will move in the same direction as the kick and spin about the midpoint (center of mass) as it moves. If you give the stick a kick right at its center it will move without spinning. Try it yourself by putting a plastic ruler on a table and giving it sharp kicks with your finger at different points along its length. Friction will eventually stop the motion, but observe what happens immediately after you deliver the kick.

3. Dec 22, 2017

### Erunanethiel

Lets say i have three sticks. One has it's center of mass in the middle, the other has it offset to the right and the last one has it offset to the left. Which one of the three sticks has the most likelihood of it's right side going backwards when the stick is pushed on it's left side?

4. Dec 22, 2017

### kuruman

It seems that we have a different understanding what "center of mass" means. Can you draw a picture of the three sticks that you mentioned?

5. Dec 22, 2017

### Erunanethiel

I cant upload pictures because I am on mobile but I can explain.

The sticks that have their centers of gravity off to one side could be made with two different materials on each side, one denser than the other, or have a metal ball on the side where the COM is, whilst the stick with COM in the middle is uniform

6. Dec 22, 2017

### kuruman

OK, let's say you have a spherical lollipop with a very light handle so that the CM is essentially at the center of the sphere. You want to set it in motion so that it does what?

7. Dec 22, 2017

### Erunanethiel

I want the handle bit to go backwards, but we need a bit of the handle to stick above the lollipop as well to be able to push on that bit

Last edited by a moderator: Dec 22, 2017
8. Dec 22, 2017

### kuruman

I am not sure what you mean by "backwards". Here is a picture of a lollipop in space. Please explain how you define the forward and backward direction in terms of "up", "down", "left" and "right" as related to the figure. I have labeled the tip of the stick as "A" and the center of mass as "CM".

9. Dec 22, 2017

### Erunanethiel

I want to know the optimal position for cm in order for point "B" to initially go "down" when force is applied at point "A"

10. Dec 22, 2017

### PeroK

When you give an impulse to one end of the rod, the COM moves forward and the object rotates around the COM. The initial velocity of the other end if the rod is the sum of the forward velocity of the COM and a backwards velocity from the rotation.

Question: what mass distribution will result in the other end of the rod initially moving backwards from its starting position with the greatest speed?

Suggested simpler version: you have a uniform rod of mass $M$ and a mass $m$ that can be attached to the rod at any point. Where do you attach the mass $m$ to maximise the backwards speed, as above?

How much of this can you work out for yourself? Do you know about the moment of inertia?

11. Dec 22, 2017

### Erunanethiel

Thank you for rephrasing it for me.

I think middle would be the answer, but I am most likely wrong

12. Dec 22, 2017

### PeroK

Even the simpler version is quite complicated I think. Interesting question.

In the middle is as good a guess as any.

13. Dec 22, 2017

### Erunanethiel

The more I think about it, it makes more sense to me that center of mass being closer to the side where we applied the impulse would result in the fastest rearward acceleration of the other side, but up to a point

14. Dec 22, 2017

### jbriggs444

How much of the stick's mass can you concentrate at the center of mass? Can you see what sort of effect concentrating the mass versus spreading it out would make?

15. Dec 23, 2017

### PeroK

Actually, the general problem is simpler. You need almost all the mass concentrated at one point.

You can't just guess that point. You need to calculate the torque and the resultant velocity of the end point.

What's your level of physics knowledge?

16. Dec 23, 2017

### Erunanethiel

I guess we need as little mass as possible on the side "B" so it would rotate "backwards" with the greatest possible velocity

17. Dec 23, 2017

### Erunanethiel

My physics education is not enough to tackle this.

Can we calculate it using the 10 cm stick with the force applied at point "zero"?

Do you reckon it would be closer to the edge the force is applied, in the middle, or closer to the side which the force isn't applied?

Last edited by a moderator: Dec 23, 2017
18. Dec 23, 2017

### PeroK

It turns out you want all the mass in the middle of the rod.

19. Dec 23, 2017

### Erunanethiel

With mass concentrated all in the middle with as little weight as possible on either side of the stick right? Does how heavy the end of the sticks make a difference as long as the Com is in the middle?

20. Dec 23, 2017

### jbriggs444

Take two extremes -- a heavy ball with two sticks on opposite sides or two heavy balls with a stick between. The moment of inertia and, therefore, the amount of angular acceleration for a given torque is different for the two.