# Ball colliding with an arm of an object that can rotate to it's axis

• Xcrypt
In summary, to properly code a physics-based minigolf game with a spinner object, you will need to calculate the angular momentum of the spinner before and after the collision using its moment of inertia and angular velocity, as well as the linear momentum of the ball before and after the collision using its mass and velocity. These calculations will help determine the new angular velocity of the spinner and the new velocity of the ball after the collision. Keep in mind that rotational momentum and linear momentum are different and must be calculated separately.
Xcrypt
http://imageshack.us/photo/my-images/195/spinner.png/
^this is the object/spinner I am referring to.

I am trying to code a physics based minigolf game in which a ball should be able to collide properly with the spinner object and the arms of it.
However I am lacking in physical knowledge to do so.

This is the model I currently have:

1) When the ball hits the spinner, a point gets defined where the ball hits the spinner. Of this point on the spinner, there is a tangential velocity bound to it which I have put in a vector.

2) Then, I projected the ballVelocityVector onto that tangentialVelocity Vector, and get a new vector: ballProjectedVelocityVector

3) After that, momentum gets defined:
ballProjectedMomentumVector = ballProjectedVelocityVector * ballMass
spinnerPointMomentumVector = pointTangentialVelocityVector * spinnerMass [probably where it goes wrong?]

4) Then new velocities get defined for the ballProjectedVelocityVector and the spinnerPointTangentialVelocityVector
Using:
va = [Cr*ma*(ub-ua)+ma*ua+mb*ub]/(ma+mb)
where:
va is the final velocity of the first object after impact
vb is the final velocity of the second object after impact
ua is the initial velocity of the first object before impact
ub is the initial velocity of the second object before impact
ma is the mass of the first object
mb is the mass of the second object
Cr is the coefficient of restitution (which I have set for a near-perfect non-elastic collision (0.05) )

5) The spinner gets a new angular velocity: (the new spinnerPointTangentialVelocityVectorLength / distance from that point to the axis of the spinner)
The ball gets a new velocityVector: (the new ballProjectedVelocityVector + (the old ballVelocityVector[projected onto the vector perpendicular to the projected velocity]) )

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However, this model I am using is not quite accurate, since if 'the point where the ball hits the spinner' is closer to the axis, the MORE angular rotation the spinner will get with this model.
Does anyone know what I am doing wrong / what steps I should take to determine the proper new angular velocity of the spinner after collision and the new velocity of the ball after collision?

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In explaining, please make try to do so so I can understand, because although I am very interested in physics and learning, my current knowledge is still very low.

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Thanks a lot for the help! :)

Last edited:
One thing to keep in mind is that rotational momentum is different from linear momentum. The angular momentum of the spinner can be calculated using the following equation:L = I * ω where L is the angular momentum of the spinner, I is its moment of inertia, and ω is its angular velocity. When the ball collides with the spinner, the angular momentum of the spinner will change. In order to calculate this, you need to calculate the linear momentum of the ball. This can be calculated using the following equation:p = m * v where p is the linear momentum of the ball, m is its mass, and v is its velocity. Once you have the linear momentum of the ball, you can calculate the change in angular momentum of the spinner. This can be done using the following equation:ΔL = p * r where ΔL is the change in angular momentum, p is the linear momentum of the ball, and r is the distance from the point of contact to the axis of rotation of the spinner. Now that you know the change in angular momentum of the spinner, you can calculate the new angular velocity of the spinner using the following equation:ω = (L + ΔL) / I where ω is the new angular velocity, L is the initial angular momentum, and I is the moment of inertia of the spinner. Finally, you can calculate the new velocity of the ball by using the following equation: v = p / m where v is the new velocity of the ball and p is the linear momentum of the ball. I hope this helped!

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

The conservation of angular momentum states that the total angular momentum of a system remains constant unless acted upon by an external torque. This means that when a ball collides with an arm of an object that can rotate on its axis, the total angular momentum of the system before and after the collision will be the same.

## 2. How does the angle of collision affect the rotational motion of the object?

The angle of collision plays a crucial role in determining the rotational motion of the object. If the ball collides perpendicular to the arm, it will transfer all of its angular momentum to the object and cause it to rotate. However, if the ball collides at an angle, only a component of its angular momentum will be transferred, resulting in a change in the direction of the object's rotation.

## 3. What is the difference between elastic and inelastic collisions in terms of rotational motion?

In an elastic collision, the total kinetic energy of the system is conserved, and the objects bounce off each other without any loss of energy. This means that the ball will transfer all of its angular momentum to the object, resulting in a change in its rotation. In an inelastic collision, some of the kinetic energy is lost, and the objects stick together after the collision. This means that the rotational motion of the object will be affected, but not as significantly as in an elastic collision.

## 4. How does the moment of inertia of the object affect the collision?

The moment of inertia, or the object's resistance to rotational motion, affects the collision by determining the object's rotational speed after the collision. A higher moment of inertia means that the object will rotate at a slower speed after the collision, while a lower moment of inertia will result in a faster rotation.

## 5. Can the ball and object rotate in opposite directions after the collision?

Yes, it is possible for the ball and the object to rotate in opposite directions after the collision. This can happen if the ball collides with the arm at an angle, causing a change in the direction of the object's rotation. In this case, the ball will continue to rotate in its original direction, while the object will rotate in the opposite direction.

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