# Moment of inertia and rotational speed of a ball

deluksic
Hey I'm making some kind of simulation... (in game maker) Ball collisions, ball to wall(friction)etc.

So I'm asking: how do i calculate rotational speed if i know r, mass, and distance to where is force being applyed?

I know that moment of inertia for a ball is 2/3*m*r2 and have no idea how to use it...

friction is also a problem.. i dont know how to calculate friction with wall if i know friction koeficient...

(sry for any mistake, im not from england)

## Answers and Replies

timthereaper
The kinetic energy of a rotating object is KE=(Iw^2)/2, where I is the moment of inertia about the centroid of the object and w is the angular velocity. If you have a force being applied to the outside of the ball, you can get the torque by using T=r x F. You can then use T=I*a, where the I is the same I as before and a is the angular acceleration.

The frictional force is given as F=mu*N, where mu is the coefficient of friction and N is the force of the wall pushing back on the object.

Hope this gets you started.

deluksic
hmm ill try to understand all that, put it in code than tell you...

deluksic
few questions...

is that aceleration in radians or degrees?
x is cross product?

that frictional force is maximal friction and i need actuall friction when ball hit the wall with speed on an angle...

timthereaper
I believe the acceleration is in radians. And yes, the x is cross product.

AFAIK, you'll have to do an impulse force calculation or something to solve for the normal force of the wall because the force the ball is hitting with wall with is changing with time. The normal force is the force perpendicular to the wall, so if the ball is hitting the wall with a force at an angle, you can just get the component in the direction perpendicular to the wall using a F cos theta or F sin theta (however you're measuring your theta). That will be the normal force and you can sub that into the F=mu*N.

deluksic
yes i know that... but that IMPULSE is confusing me... impulse is actually F=(m/\v)/t right?
t in my program is actually one step of simulation so force that will be applying is just mv?

also i managed to make it out with rotations now how do i calc that actuall speed of center of mass when force is being applyed? it cant be the same if u pull an object on a corner or in center of mass...

Bassalisk
Rotating rigid bodies are world for it self. But here are some helpful tips.

I believe that u are familiar with dynamics, newton etc. In translation-like motions you have mass (m) and speed (v).

Now think of it this way. Physics has to work in the same laws, little bit different and adjusted but same in their intention.

What is mass for translation, that is moment of inertia for rotating bodies. What is speed for translation(v) that is angular speed for rotating bodies (w). What is force for translation, that is torque for rotating bodies.

same for momentum, acceleration etc. These analogies could help you start.

if you want to study this, and really learn it here are some helpful links.

http://ocw.mit.edu/courses/physics/...chanics-fall-1999/video-lectures/lecture-19/"
http://ocw.mit.edu/courses/physics/...chanics-fall-1999/video-lectures/lecture-20/"
http://ocw.mit.edu/courses/physics/...chanics-fall-1999/video-lectures/lecture-21/"

After these 3 50 minutes lectures, i think you will have all you need for you project, there is more if you are interested

Last edited by a moderator:
deluksic
now i see that it is totaly the same if i pull something for a corner or in center of mass thanks! That MIT teacher is very good! (and funny xD..)

Bassalisk
now i see that it is totaly the same if i pull something for a corner or in center of mass thanks! That MIT teacher is very good! (and funny xD..)

Pulling an object to make it move only depends of the angle of that force and the direction of the movement.

Bassalisk
yes if ur interested u can download my first test of it to see what it looks like :D