# Can spinning motion be converted into linear motion?

Hi, I've been working on a school project which involves investigating the momentum before and after a collision between two steel balls.

E.g. we have Ball A (moving) and Ball B (stationary), which are of identical mass. Ball A collides into Ball B. What we have observed is that Ball B then moves off with almost the same velocity as A had originally, but A does not stop, but retains a small (but significant) velocity, i.e. the final momentum is greater than the initial momentum.

One possible cause of this is that A's spinning motion gets converted into linear motion (hence increasing its linear velocity). But I just wanted to check that this is actually possible? And how does it happen?

Thanks, sorry if this question is rather basic, I'm still in highschool :)

Staff Emeritus
Ever ride a bicycle or drive a car? The wheels turn spinning motion into linear motion.

• billy_joule and rootone
russ_watters
Mentor
[deleted: not the point]

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I think what the op is asking is; if it is possible for rotational kinetic energy to be converted to translational kinetic energy in a collision.
If I understand correctly, he is saying that he has observed two steel balls colliding and after the collision the total translational kinetic energy is higher than before the collision and asking if some of that energy may have been rotational before the collision and now is translational.
I think it is an interesting question!
My answer is yes, that is possible as the total of rotational KE and translational KE are conserved. (conditioned on not taking into account here other forms of energy such as heat and sound and light)
So if the ball doing the striking was spinning without sliding before the collision and the target ball moves away mostly sliding with little spinning, the total translational KE may be higher after the collision than before, but the rotational KE will be lower. Total kinetic energy remains unchanged (with the same condition stated earlier).

robphy
Homework Helper
Gold Member
In analyzing such a problem [neglecting friction], it might be good to realize that if a particular collision occurs, then the time-reverse of that collision can also occur.
In addition, a more complete analysis of this collision of presumably rigid non-point objects will also involve the conservation of angular momentum and non-head-on collisions.

jbriggs444
Homework Helper
You have observed that ball A has a non-zero final velocity. But you have not measured the difference between A's initial velocity and B's final velocity. How can you assert that total linear momentum has increased?

For a ball that is rolling without slipping, there is a fixed ratio between the ball's angular momentum about its center and the ball's linear momentum. Since the two balls are identical, this ratio will be the same for each. For a ball that whose rolling rate and linear speed do not match, it will require a rotational impulse (a torque applied over time) to get them to match.

During the collision, linear momentum is be transferred from ball A to ball B.

Claim: The resulting imbalance between linear momentum and rolling speed on each ball will be equal and opposite. It will require equal and opposite rotational impulses to get them to match. Because the balls have equal radius, this means equal and opposite linear impulses. That means that momentum will be conserved while ball A spins down (and speeds up) and ball B spins up (and slows down).

During the collision, steel-on-steel friction will cause both balls to experience a slight backwards torque around their respective centers of mass. This can only act to reduce the final momentum of the system.

A.T.