# Calculating angular velocity of a ratatable bar in inelastic collision

In summary, when a bullet is shot horizontally at the edge of a rotatable bar, the bar experiences an angular velocity of 0.17 m/s.

## Homework Statement

1 m long rotatable bar with a mass of 2 kg is held on vertical stick that goes through its center of gravity. A bullet with mass 0.2 kg is shot with a speed 1 m/s horizontally at the edge of the bar. After the collision the bullet lodges into the bar. Calculate the angular velocity of the bar after the collision, if the bar was at rest at the beginning?

## Homework Equations

Conservation of the angular moment

## The Attempt at a Solution

mRv= (MR + mR + I) ω

ω= mRv / (MR² + mR² + MR²/12)
ω= mv / (MR + mR + MR/12)
ω= 0.17 m/s

Are my calculations correct?

ω= mRv / (MR² + mR² + MR²/12)
ω= 0.17 m/s
Are my calculations correct?[/SUB]
Why are there three terms in the denominator? You are calculating angular momentum about the pivot which is also the CM of the rod. In the denominator you need only two terms, the angular momentum of the rod about the pivot (or its CM) and the angular momentum of the bullet about the pivot. Is "R" the length of the rod or is it the distance of the bullet from the pivot?

mRv= (mR + I) ω

ω= mRv / (mR² + MR²/12)
ω= 0.19 m/s

"R" is half the length of the rod, in other words the distance of the bullet from the pivot.

Are now my calculations correct?

The moment of inertia of a rod of mass M and total length L about its mid point is

$$I=\frac{1}{12}ML^2$$

what should the formula look like if you used R instead of L?

kuruman said:
The moment of inertia of a rod of mass M and total length L about its mid point is

$$I=\frac{1}{12}ML^2$$

what should the formula look like if you used R instead of L?

I think it should be like this ω= mRv / (mR² + M(2R)²/12)?

And the answer is now:

ω= 12 m/s

I didn't put in the numbers, but the algebraic expression you have is correct.

Thank you very much!

## 1. How do I calculate the angular velocity of a rotatable bar in an inelastic collision?

To calculate the angular velocity of a rotatable bar in an inelastic collision, you will need to know the moment of inertia of the bar, the mass of the bar, and the initial and final angular velocities. Use the formula: ωf = (Iωi + mvr) / (I + mr^2), where ωf is the final angular velocity, ωi is the initial angular velocity, I is the moment of inertia, m is the mass, v is the linear velocity, and r is the distance from the axis of rotation.

## 2. What is the moment of inertia and how does it affect the calculation of angular velocity?

Moment of inertia is a measure of an object's resistance to changes in its rotation. It depends on the mass and distribution of mass around the axis of rotation. The larger the moment of inertia, the more difficult it is to change the object's angular velocity.

## 3. How does the mass of the bar impact the calculation of angular velocity?

The mass of the bar affects the calculation of angular velocity because it is a factor in the moment of inertia. A larger mass will result in a larger moment of inertia, making it more difficult to change the object's angular velocity.

## 4. What is an inelastic collision and how does it differ from an elastic collision?

An inelastic collision is a type of collision in which kinetic energy is not conserved. In other words, some of the initial kinetic energy is lost during the collision, typically due to the objects sticking together or undergoing deformation. In contrast, an elastic collision is a type of collision in which kinetic energy is conserved. This means that the total kinetic energy of the objects before and after the collision remains the same.

## 5. Can the formula for calculating angular velocity be applied to other objects besides rotatable bars?

Yes, the formula for calculating angular velocity can be applied to any object that has a defined moment of inertia and experiences an inelastic collision. This could include objects such as wheels, discs, or cylinders. However, the specific values for moment of inertia and other variables may differ depending on the shape and mass distribution of the object.

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