Why is the angular momentum negative in a disk and stick collision?

In summary, the angular momentum of the ball is determined by the equation ## L_{f} = -rm_{d}V_{df} + I\omega## rather than ## L_{f} = rm_{d}V_{df} + I\omega ## due to the standard of taking anticlockwise rotation as positive. The diagram may be misleading as it indicates clockwise rotation, but understanding that it will come out negative is important.
  • #1
hhjjy
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Homework Statement
A 2.0-kg disk traveling at 3.0 m/s strikes a 1.0-kg stick of length 4.0 m that is lying flat on nearly frictionless ice as shown in the overhead view of Figure 11.12a. The disk strikes at the endpoint of the stick, at a distance r = 2.0 m from the stick’s center.

Assume the collision is elastic and the disk does not deviate from its original line of motion. Find the translational speed of the disk, the translational speed of the stick, and the angular speed of the stick after the collision. The moment of inertia of the stick about its center of mass is 1.33 kg m^2?
Relevant Equations
## L_{f} = L{i} ##
## L = \vec{r} \times \vec{p} ##
## |L| = mvr \sin{\theta}##
figure 11.12
1640483489226.png


I need someone to explain why the angular momentum of the ball is ## L_{f} = -rm_{d}V_{df} + I\omega## rather than ## L_{f} = rm_{d}V_{df} + I\omega ##. How to distinguish the sign of the angular momentum?p.s. ##\Delta\vec{L}_{total} = \vec{L}_{f} - \vec{L}_{i} = (-rm_{d}v_{df} + I\omega) - (-rm_{d}v_{di}) ##
1640483625566.png
 
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  • #2
hhjjy said:
explain why the angular momentum of the ball is ## L_{f} = -rm_{d}V_{df} + I\omega## rather than ## L_{f} = rm_{d}V_{df} + I\omega ##. How to distinguish the sign of the angular momentum?
## L_{f} = -rm_{d}V_{df} + I\omega## is the final angular momentum of ball plus stick. That of the ball is just ## L_{f} = -rm_{d}V_{df} ##
As is a common standard, the author is taking anticlockwise rotation as positive. What is misleading is that the diagram shows ##\omega## as being measured clockwise. To be correct, it should indicate the rotation as anticlockwise, but understanding that it will come out negative.
 
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  • #3
Ok, thanks.
 
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1. Why is angular momentum negative in a disk and stick collision?

Angular momentum is a measure of an object's rotational motion. In a disk and stick collision, the stick is typically attached to the disk at one end and free to rotate at the other end. When the collision occurs, the stick exerts a force on the disk, causing it to rotate. The direction of this rotation is opposite to the direction of the stick's movement, resulting in a negative angular momentum.

2. How is angular momentum calculated in a disk and stick collision?

Angular momentum is calculated using the formula L = Iω, where L is the angular momentum, I is the moment of inertia, and ω is the angular velocity. In a disk and stick collision, the moment of inertia is dependent on the mass and distribution of mass in the objects, and the angular velocity is determined by the rotational motion caused by the collision.

3. Can angular momentum be positive in a disk and stick collision?

Yes, it is possible for angular momentum to be positive in a disk and stick collision. This can occur if the stick is attached to the disk in a way that causes the disk to rotate in the same direction as the stick's movement.

4. What factors affect the magnitude of angular momentum in a disk and stick collision?

The magnitude of angular momentum in a disk and stick collision is affected by several factors, including the mass and distribution of mass in the objects, the speed and direction of the stick's movement, and the angle at which the stick makes contact with the disk.

5. How does the conservation of angular momentum apply to a disk and stick collision?

The conservation of angular momentum states that the total angular momentum of a system remains constant, as long as no external torques act on the system. In a disk and stick collision, the initial angular momentum of the system is equal to the final angular momentum after the collision, as long as no external forces or torques are present.

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