# Simple Question(s) About Angular Momentum

Hi all.

I'm a game programmer with very little exposure to physics. I had one class in high school that spent 6 weeks "teaching me" what we learned on the first day in calculus class about velocity and acceleration. So please be patient :).

For something I'm programming, I'm trying to achieve realistic interactions between rigid bodies. I'm having trouble understanding physics of rotations.

If I had a pencil floating in space, outside of gravity, air resistance, etc., and I pushed on the eraser, would the pencil rotate around some point (probably the centroid of mass), or would the whole pencil move forward, just as though I had split the force and pushed on both the eraser and on the pencil lead?

All discussions I have found online seem to expect I have a pivot/fulcrum/etc. I have always assumed that in their absence there is no rotation, and that things like lamp posts tipping over when you push the top are because of a pseudo-fulcrum caused at the base by friction. However, the simulation at http://www.myphysicslab.com/collision.html has me worried that I've got this all wrong.

Yet if this is so, then why do you need to use both your thumb and your index finger to turn a screw, rather than just pushing on one side?

Aside from this particular question, in general does anybody have good advice for a computer programmer / mathematician with no physics training to get up to speed on "everything" there is to know about Newtonian Mechanics? Everything I can find on the internet either seems to be the limited "practical" subset they teach in High School (i.e. all angular momentum discussion seems to suppose a lever arm with some part of the object rigidly anchored), or else so rigorous as to be useless to someone just setting out (notational myopia that, necessary for correctness and the specialist, nonetheless occludes comprehension and overview-understanding).

Thanks!

dacruick
If I had a pencil floating in space, outside of gravity, air resistance, etc., and I pushed on the eraser, would the pencil rotate around some point (probably the centroid of mass), or would the whole pencil move forward, just as though I had split the force and pushed on both the eraser and on the pencil lead?

it would be a mix of both of those things. Imagine you have a metal cylinder on an icy near frictionless surface. and you push on one end of that cylinder, do you think it will rotate along an axis or it will slide and rotate?

I also believe that it will depends how hard you strike the eraser.

I'm not sure about the cylinder. I was playing around with a pepper shaker on the floor a moment ago, and got quite confused. Clearly with small forces it slides, and larger ones it topples over. This is why gravity and friction are upsetting my thought experiments.

I'm guess from your reply then that the force is transformed into a translation ("Net Force"?) component that slides it, and an angular force that rotates it. Do these two things sum together, or are they 'separate but equal'?

dacruick
umm they dont sum together. their energies will sum to be the total energy of the system but I think that is the only relationship. Something tells me that the pencil will have translational momentum and angular momentum. you know what though, maybe I'm wrong.

I know you don't have a strong physics background but try to stick with me here. Imagine that pencil in space and your finger pushing it. When I imagine that I see no possible way that the pencil wouldn't have translational momentum. But, its possible that if the applied force is perpendicular to the pencil. and instantaneous, that it would only rotate. Think about pushing your finger to the pencil and the impact not being instantaneous. That means that halfway through your pushing of the pencil, the pencil is already rotated and the force applied is no longer in the direction of its angular velocity. I think that is what would cause the translational momentum. But if the applied force is perpendicular and instantaneous, it might not rotate. I am not sure about this at all.

Try looking at the wiki on torque to get a sense for your answer. Torque is defined as the vector cross product of the vectors r and F, where F is the force and r defines the vector displacement between the point A where the force is applied and point B where the torque is measured. The point B is often a fixed point of a fulcrum, but is by no means required to be. For a free body (like your pencil example), the natural point to measure torque from is the center of mass.

As you can see from the wiki page, the magnitude of the torque is just the length of the lever arm times the perpendicular component of the applied force. So, if you push on the eraser when the pencil is pointing exactly away from you, there will be no torque, and therefore no rotation; all the force will go into generating linear momentum. You will get maximum torque (and maximum rotation) when the pencil is exactly perpendicular to you ... then all of the applied force will go into generating angular momentum. If the pencil is at some other angle with respect to the applied force, then you will get a combination of linear and angular momentum.

HTH

dacruick
so my speculation was correct. If you can apply instantaneous force perpendicular to the pencil, you can produce only angular momentum.

opsb
If you apply an impulse (magnitude I) to a pencil, the net linear momentum of the pencil must increase, according to Newton's third law, wherever the impulse is applied.

In the example, we push the end of the pencil. The impulse acts along a line perpendicular to the pencil. Taking moments about the centre of mass, the angular impulse is RI (for a pencil of length 2R).

So the final linear momentum is I, and the final angular momentum is RI.

The pencil (mass M) moves with a linear velocity of I/M , and with an angular velocity of 3I/MR

To clarify, I was thinking of the force being applied perpendicular to the pencil.

Mentor
Yes. I believe that SpectraCat made an error. As opsb noted, an applied force always produces a change in linear momentum. There's no way to hit the pencil with a single force and only produce a change in angular momentum.

Billy Berakus
Hi,

Just for the fun of it... I took your experiment to heart and jumped on a space ship and headed into space to achieve an answer.

The space ship -> my air hockey table -> I attached the pencil to the puck... close to center to the best of my ability. (certainly flawed) I proceeded to hit the eraser to send the pencil into a spin.

It did as discussed, it spun plus the mass moved in the exact direction that I hit the side of the eraser. (Interesting!)

It appeared that the pencil absorbed 75% of the force or more related to the spin as when I hit the mass with aprox the same amount of force near center, the mass traveled at a much greater speed with no spin.

Thought you may find this interesting.

GRDixon
If I had a pencil floating in space, outside of gravity, air resistance, etc., and I pushed on the eraser, would the pencil rotate around some point (probably the centroid of mass), or would the whole pencil move forward, just as though I had split the force and pushed on both the eraser and on the pencil lead?

It depends on whether you push on the eraser along a line that passes through the pencil's center of mass, or that misses the center of mass. In the first case the pencil would simply accelerate according to F=ma. In the second case the pencil would accelerate and begin to rotate around its center of mass, the speed of rotation depending upon the angle between the applied force and the pencil's midline. As for getting up to speed, I would recommend a good introductory text to Newtonian mechanics. You can usually see samples of what's inside the books on www.amazon.com, among other online bookstores. Pick one that you feel comfortable reading. And by all means, pick one that has problems and answers, so that you can get some hands-on experience with the concepts. Good luck. Modeling physics on a computer can be very rewarding.