Angular Momentum before and after being hit with a ball of clay

In summary: Question 1 is impossible to answer without knowing how to calculate the angular momentum of the clay relative to the wheel's axis.
  • #1
Qnslaught
8
0

Homework Statement



A device consists of eight balls each of mass 0.7 kg attached to the ends of low-mass spokes of length 1.8 m, so the radius of rotation of the balls is 0.9 m. The device is mounted in the vertical plane. The axle is held up by supports that are not shown, and the wheel is free to rotate on the nearly frictionless axle. A lump of clay with mass 0.23 kg falls and sticks to one of the balls at the location shown, when the spoke attached to that ball is at 45 degrees to the horizontal. Just before the impact the clay has a speed 6 m/s, and the wheel is rotating counterclockwise with angular speed 0.10 radians/s.

(a) Which of the following statements are true about the device and the clay, for angular momentum relative to the axle of the device?

The angular momentum of the falling clay is zero because the clay is moving in a straight line.

The angular momentum of the device is the same before and after the collision.

The angular momentum of the device + clay just after the collision is equal to the angular momentum of the device + clay just before the collision.

The angular momentum of the device is the sum of the angular momenta of all eight balls.

Just before the collision the angular momentum of the wheel is 0.



Homework Equations





The Attempt at a Solution



I'm pretty sure the clay has angular momentum, so I think the first one is right. I'm not sure about the second one but I don't think it's right. I think the angular momentum of the system stays the same. I think the momentum of the device is the sum of all the balls. And I don't think the angular momentum of the wheel is 0.
 
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  • #2
Angular momentum (like torque) needs a reference point. The problem gives none. However, let us assume that the angular momentum is referred to the axis of the wheel. How do you find the angular momentum of a moving point mass with respect to some reference point?
 
  • #3
Well if I used that as a reference point then, the clay falling would have an angular momentum right?
 
  • #4
To answer question 1 you need to know how to calculate the angular momentum of the clay relative to the wheel's axis. If you do the calculation and the answer is zero, then the clay has no angular momentum. If you do the calculation and the answer is not zero then the clay does have angular momentum.

What is the definition of angular momentum for a point mass?
 

1. What is Angular Momentum?

Angular Momentum is a physical quantity that describes the rotation or spinning motion of an object. It is a vector quantity, meaning it has both magnitude and direction.

2. How is Angular Momentum calculated?

Angular Momentum is calculated by multiplying the moment of inertia of an object (a measure of its resistance to rotational motion) by its angular velocity (the rate at which it is rotating) and the direction of rotation.

3. What happens to Angular Momentum before and after being hit with a ball of clay?

Before being hit with a ball of clay, the angular momentum of an object is determined by its initial moment of inertia and angular velocity. After being hit with a ball of clay, the moment of inertia may change due to the added mass, and the angular velocity may also change depending on the direction and force of the impact. Therefore, the overall angular momentum of the object will be different before and after the impact.

4. How does the conservation of Angular Momentum apply in this scenario?

The conservation of Angular Momentum states that the total angular momentum of a system remains constant unless acted upon by an external torque. In the scenario of being hit with a ball of clay, the overall angular momentum of the object may change, but the total angular momentum of the system (object + clay) will remain the same.

5. Why is Angular Momentum important in physics?

Angular Momentum is important in physics because it helps us understand and predict the rotational motion of objects. It is also a fundamental principle in the laws of conservation of energy and momentum, which are essential in understanding the behavior of physical systems.

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