Finding Force from Linear & Angular Momentum in Elastic Collision

[TheDonk]

Let's say I have a stationary object that gets hit on a flat edge by a sharp point of a moving object. Assume that the moving object also has an linear and angular momentum. Assume that the objects have uniform density, there is no deformation, no friction, and that the collision is ellastic. Also do not assume that the line from the centerpoint of the moving object to the contact point is parallel to the direction of the linear momentum. With all possible information, (momentum, center point, etc) how would you find the force that the moving object applied to the stationary object?

 

[shyboy]

To find the force you need to know how the objects interacted during the collision. That means the you need to know what kind of deformation existed.

 

[charng]

To find the force applied by the moving object to the stationary object in this elastic collision scenario, we can use the principle of conservation of linear and angular momentum. This principle states that the total momentum before the collision is equal to the total momentum after the collision.

First, we can calculate the linear momentum of the moving object by multiplying its mass by its velocity. We can also calculate the angular momentum by multiplying the moment of inertia (determined by the object's shape and mass distribution) by its angular velocity.

Next, we can determine the change in linear and angular momentum of the moving object after the collision. This can be done by subtracting the initial momentum values from the final momentum values.

Then, using the conservation of momentum principle, we can equate the change in linear and angular momentum of the moving object to the change in linear and angular momentum of the stationary object. This allows us to solve for the unknown force applied by the moving object to the stationary object.

It is important to note that in this scenario, the direction of the force will be perpendicular to the line connecting the center point of the moving object and the contact point on the stationary object. This is because the point of contact is the point of rotation for the angular momentum of the moving object and the force will act to change the object's angular momentum.

In conclusion, by using the principles of conservation of linear and angular momentum, along with the known properties of the objects involved in the collision, we can determine the force applied by the moving object to the stationary object in an elastic collision.