# Combination of Linear and Angular momentum

• ness9660
In summary, a solid cylinder of mass 42 kg and radius 0.14 m is pivoted on a frictional axle. A particle of mass 4.2 kg and initial velocity 17 m/s collides with the cylinder, sticking to it. Before the collision, the cylinder was not rotating. To find the angular velocity after the collision, you can use the equation L = mvR, where L is the initial angular momentum, m is the mass of the particle, v is its initial velocity, and R is the radius of the cylinder.
ness9660
A solid cylinder of mass M = 42 kg, radius R = 0.14 m and uniform density is pivoted on a frictional axle coaxial with its symmetry axis. A particle of mass m = 4.2 kg and initial velocity v0 = 17 m/s (perpendicular to the cylinder's axis) flies too close to the cylinder's edge, collides with the cylinder and sticks to it. Before the collision, the cylinder was not rotating. What is its angular velocity after the collision? Answer in units of rad/s.

Im lost on forming the equation for this problem. Combination of angular momentum problems have been fairly easy using Li/Lf, I thought I would try something similar like this:

Li=m*v for the momentum of the object, and nothing for the cylinder since it is at rest
Lf= (1/2)m1*R^2 + m2R^2

Where m1 is the mass of the cylinder and m2 that of the object.

Then as usual doing w=Li/Lf, however this produces a wrong answer. I think I am missing a key concept here in translating linear momentum to angular momentum because what I am doing is turning out very wrong.

Thanks

The initial angular momentum is $$mvR$$ assuming the the particle hits right at the top edge of the cylinder.

$$L = I\omega = mvR$$

asrodan said:
The initial angular momentum is $$mvR$$ assuming the the particle hits right at the top edge of the cylinder.

$$L = I\omega = mvR$$

Ah, thank you very much for the help.

## 1. What is the definition of combination of linear and angular momentum?

The combination of linear and angular momentum is a physical quantity that describes the motion of an object in terms of both its linear velocity and its rotational velocity. It is a vector quantity that takes into account both the linear and angular components of an object's momentum.

## 2. How is the combination of linear and angular momentum calculated?

The combination of linear and angular momentum is calculated by taking the product of an object's mass, linear velocity, and the distance from the axis of rotation to the point of application of the linear force. This is then added to the product of the moment of inertia and the angular velocity of the object.

## 3. What is the conservation of momentum principle?

The conservation of momentum principle states that the total momentum of a closed system remains constant, unless acted upon by an external force. This means that the total combination of linear and angular momentum of a system will remain the same before and after a collision or interaction.

## 4. How does the combination of linear and angular momentum affect the motion of an object?

The combination of linear and angular momentum affects the motion of an object by determining its overall momentum and the distribution of this momentum between its linear and angular components. This can affect the object's rotation, stability, and trajectory.

## 5. What are some real-world examples of the combination of linear and angular momentum?

Some real-world examples of the combination of linear and angular momentum include a spinning top, a ball rolling down a hill, and a figure skater performing a spin. In all of these examples, both linear and angular momentum are present and interact to determine the overall motion and stability of the objects.

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