# What is the total kinetic energy of the rod?

• ccarit3007
In summary, the conversation discusses the total kinetic energy of a uniform rod rotating at an axis. The suggested solution includes both rotational and translational energy, but the answer choices do not match. It is noted that the rod can be viewed as having pure rotation or both rotation and translation, with the same resulting answer. The expression provided for rotational KE is questioned, and it is suggested to express everything in terms of the angular velocity ω.
ccarit3007

## Homework Statement

Uniform rod rotates at axel. What is the total kinetic energy of the rod?

## Homework Equations

deltaKrot = 1/2Iw^2
deltaKtrans = 1/2mv^2

## The Attempt at a Solution

I believe the rod has both rotational as well as translation energy because the rod is not rotating about its center of mass. I end up getting 1/2ML^2w^2+1/2Mv^2 which is not the answer choices. (The answer is B).

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ccarit3007 said:
I believe the rod has both rotational as well as translation energy because the rod is not rotating about its center of mass.
You can view the rod as having both rotational KE about the center of mass and translational KE of the center of mass. Or you can view the rod as in pure rotation about the given axis. Your choice. Either way, the answer will be the same.

ccarit3007 said:
I end up getting 1/2ML^2w^2+1/2Mv^2 which is not the answer choices.
Two points: (1) How did you get that expression for the rotational KE? (2) Realize that ω and v are related. Express everything in terms of ω.

## 1. What is kinetic energy?

Kinetic energy is the energy an object possesses due to its motion.

## 2. How do you calculate the total kinetic energy of a rod?

The total kinetic energy of a rod can be calculated by multiplying its mass by the square of its velocity, and then dividing by 2:

KE = (1/2) * m * v^2

## 3. What are the units of kinetic energy?

Kinetic energy is measured in joules (J) in the International System of Units (SI).

## 4. Does the shape of the rod affect its kinetic energy?

Yes, the shape of the rod can affect its kinetic energy. For example, a long thin rod will have a higher kinetic energy than a short thick rod with the same mass and velocity.

## 5. What factors can influence the total kinetic energy of a rod?

The total kinetic energy of a rod can be influenced by its mass, velocity, and the external forces acting on it, such as friction or air resistance.

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