# Conversion of angular momentum to linear momentum

• ozcliff
In summary, when a bowl in motion collides at a glancing angle with another bowl at rest, the apparent pre-collision velocity is seemingly increased. This is likely due to the conservation of linear momentum, but the increase in velocity may be an illusion.
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?

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

Dale said:
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.

ozcliff said:
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.

PeroK said:
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.

Last edited:
PeroK, Nugatory, Dale and 1 other person
ozcliff said:
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.

vanhees71
PeroK said:
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!

weirdoguy

## 1. What is the definition of angular momentum?

Angular momentum is a measure of the rotational motion of an object around an axis. It is the product of an object's moment of inertia and its angular velocity.

## 2. How is angular momentum related to linear momentum?

Angular momentum and linear momentum are both conserved quantities in a closed system. This means that the total amount of angular momentum and linear momentum in a system will remain constant, even if they are converted between each other.

## 3. Can angular momentum be converted to linear momentum?

Yes, angular momentum can be converted to linear momentum and vice versa. This is known as the conservation of angular momentum and linear momentum, and it occurs when there is a change in the rotational motion of an object.

## 4. What are some examples of conversion of angular momentum to linear momentum?

One example is when a spinning top falls over and its rotational motion is converted to linear motion as it falls. Another example is the motion of a satellite around a planet, where the angular momentum of the satellite is converted to linear momentum as it moves in its orbit.

## 5. How is the conversion of angular momentum to linear momentum used in real-world applications?

The conversion of angular momentum to linear momentum is used in many real-world applications, such as in the design of rockets and spacecraft. By using the conservation of angular momentum and linear momentum, engineers can calculate the necessary forces and velocities to achieve desired trajectories and maneuvers.

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