# Conservation of angular momentum problem

• hatephysics
In summary, the rotational kinetic energy of two cylinders with the same rotational energy will be the same, regardless of their radii or masses, due to the conservation of energy. However, if the mass is different, the one with the greater mass will have a greater rotational kinetic energy. In the case of different radii, the tangential velocity will be equal, but the larger cylinder will have a smaller angular velocity. Therefore, the larger cylinder will have a greater rotational kinetic energy due to its greater mass.
hatephysics

## Homework Statement

If two cylinders have the same rotational energy, do the cylinders, though having either different radii or different masses, have the same tangential velocity?

## Homework Equations

Rotation Equations (torque, etc)

## The Attempt at a Solution

My gut feeling says yes, because of the conservation of energy.

Thank You for any help.

EDIT: My gut feeling says yes, because of the conservation of angular momentum?

If you have two identically-shaped cylinders rotating at the same speed, one made out of snow and the other made out of lead, which will have a greater rotational kinetic energy?

ideasrule said:
If you have two identically-shaped cylinders rotating at the same speed, one made out of snow and the other made out of lead, which will have a greater rotational kinetic energy?

I guess the lead one would because of the greater inertia, but what about the case with different radii. The way I see it is, they both follow .5I(omega)^2 so the larger cylinder will have a larger radius but a small angular velocity. But, tangential velocity is multiplying both radius and angular velocity so won't the tangential velocity be equal in this case?

Well, I tried using an arbitrary case and my new answer is "no" but I still don't quite get why.
In my case, I designated the radius to be multiplied by 4 and the angular momentum to be multiplied by .5

0.5Iw^2 can be rewritten as 0.5I(v/r)^2. Since I=(1/2)Mr^2 for a cylinder, KE=(1/4)Mv^2. So radius doesn't affect kinetic energy as long as mass is constant.

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

The conservation of angular momentum problem is a fundamental concept in physics that states that in a closed system, the total angular momentum remains constant. This means that the amount of rotational motion in a system will not change unless an external force is applied.

## 2. How is angular momentum conserved?

Angular momentum is conserved because of Newton's First Law of Motion, which states that an object will remain in its state of motion unless acted upon by an external force. In the case of angular momentum, the rotational motion of an object will remain constant unless an external torque is applied.

## 3. What is an example of the conservation of angular momentum?

An example of the conservation of angular momentum is the motion of a spinning top. As long as the top remains upright and in motion, its angular momentum will remain constant. If the top starts to tilt or slow down, external forces are acting upon it, causing a change in its angular momentum.

## 4. How is the conservation of angular momentum related to the Law of Inertia?

The conservation of angular momentum is related to the Law of Inertia because both concepts are based on the idea that an object's motion will not change unless acted upon by an external force. The Law of Inertia applies to linear motion, while the conservation of angular momentum applies to rotational motion.

## 5. What are the practical applications of the conservation of angular momentum?

The conservation of angular momentum has many practical applications in everyday life and in various fields of science, such as astronomy, mechanics, and engineering. For example, it is used in the design of spacecrafts, gyroscopes, and even sports equipment like bicycles and figure skates. It is also a crucial concept in understanding the motion of planets and stars in the universe.

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