Conversion of angular momentum to linear momentum

[ozcliff]

The balls used in the game of lawn bowls are biased so that they travel in a curved path of decreasing radius. When a bowl in motion collides at a glancing angle with another bowl at rest, it -appears- to increase its velocity. Due to conservation of linear momentum the post-collision velocity cannot be greater than the pre-collision velocity, yet the velocity does -appear- to increase. This may just be an illusion or is there some way that the pre-collision angular momentum is converted to linear momentum due to the collision?

 

[Dale]

Angular momentum and linear momentum are separate quantities which are each independently conserved. There is no conversion between the two.

 

[PeroK]

Angular momentum and linear momentum are separate quantities which are each independently conserved. There is no conversion between the two.

For a closed system the total linear and angular momentum are separately conserved. But, if a ball is spinning and comes into contact with a surface, the rotational angular momentum can be converted to linear momentum.

 

[PeroK]

Summary:: Can angular momentum be converted to linear momentum through the collision of rolling biased balls?

The balls used in the game of lawn bowls are biased so that they travel in a curved path of decreasing radius. When a bowl in motion collides at a glancing angle with another bowl at rest, it -appears- to increase its velocity. Due to conservation of linear momentum the post-collision velocity cannot be greater than the pre-collision velocity, yet the velocity does -appear- to increase. This may just be an illusion or is there some way that the pre-collision angular momentum is converted to linear momentum due to the collision?

I suspect this is an illusion. It may be quite a common misconception for glancing collisions that energy is gained.

The situation is different for, say, a spinning cricket ball, which can leave the surface with a greater speed - and especially a greater horizontal speed - than it had before impact.

 

[A.T.]

But, if a ball is spinning and comes into contact with a surface, the rotational angular momentum can be converted to linear momentum.

This way to phrase it just leads to confusion. Rotational and linear kinetic energy have the same dimension, so it's obvious what converting means. But angular and linear momentum don't have the same dimension, so it's not so obvious what converting means. I would not mention any converting of angular momentum to linear momentum:

- The force from the surface adds linear momentum.
- The force from the surface creates a torque that reduces the angular momentum.
- The rotational kinetic energy is converted into linear kinetic energy.

 

[A.T.]

Due to conservation of linear momentum the post-collision velocity cannot be greater than the pre-collision velocity,

Total linear momentum is conserved as a vector. If the bowl initially at rest gains velocity in one direction, the initially moving bowl can gain velocity in the opposite direction and increase its velocity magnitude. But the energy has to come from somewhere, for example from the spin of the bowl.

 

[Dale]

For a closed system the total linear and angular momentum are separately conserved. But, if a ball is spinning and comes into contact with a surface, the rotational angular momentum can be converted to linear momentum.

I would not say that one is converted to the other even in this case. The units are different so conversion doesn’t make sense. Different forms of energy have the same units, so it makes sense to convert between them, but angular and linear momentum are not different forms of momentum in that sense.

What I would say is that the external interaction provides both force and torque which change the linear and angular momentum of the system and the environment.

Edit: @A.T. said it better and faster!