Kinetic energy of rotated cylinders

In summary, the conversation discusses a figure with two rotating solid cylinders and one stationary rectangle, all with equal mass and radius. The goal is to prove that the kinetic energy of the figure is equal to 2Mv2. The solution involves calculating the rotational kinetic energy of the cylinders and adding it to the linear kinetic energy of the rectangle, resulting in a total of 2Mv2.
  • #1
steffan
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0

Homework Statement



You have a figure that is combined with three figures. Two solid cylinders and one rectangle in the middle. Like this: O[]O

The two cylinders is rotating and are not sliding, so the whole figure moves to the right. The rectangle is connected with the two cylinders. Both cylinders and the rectangle has each mass M, so it will be three masses: M1=M2=M3. Also the two cylinders has the same radius: r1=r2

Proof that the kinetic energy equals to 2Mv2 (k=2Mv2)

Homework Equations



K=1/2Mv2=1/2M(r2w2)=1/2Iw2
I=1/2Mr2 (for solid cylinders)

The Attempt at a Solution



2*1/2Iw2=2*1/2*1/2Mr2*w2=
2*1/2*1/2Mv2(energy of 2 cylinders)+1/2Mv2(energy of rectangel)=1Mv2

I don't understand why it should be 2...
 
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  • #2
hi steffan! :smile:
steffan said:
2*1/2*1/2Mv2(energy of 2 cylinders)+1/2Mv2(energy of rectangel)=1Mv2

you've only included the rotational KE of the cylinders, you must add the linear KE :wink:
 
  • #3
Oh, so it has both linear and rotational ke? Thanks alot, I didn't knew that :)
 

1. What is the formula for calculating the kinetic energy of a rotated cylinder?

The formula for calculating the kinetic energy of a rotated cylinder is E = 1/2 * I * ω^2, where E is the kinetic energy, I is the moment of inertia, and ω is the angular velocity.

2. How does the moment of inertia affect the kinetic energy of a rotated cylinder?

The moment of inertia is a measure of an object's resistance to changes in its rotational motion. The larger the moment of inertia, the more energy is required to rotate the cylinder, thus increasing its kinetic energy.

3. Is the kinetic energy of a rotated cylinder affected by its shape?

Yes, the shape of a cylinder can affect its moment of inertia, and therefore, its kinetic energy. A cylinder with a larger radius and/or mass will have a greater moment of inertia and require more energy to rotate, resulting in a higher kinetic energy.

4. Can the kinetic energy of a rotated cylinder be negative?

No, the kinetic energy of a rotated cylinder cannot be negative. Since kinetic energy is a measure of an object's motion, it is always a positive value. If the cylinder is rotating in the opposite direction, the kinetic energy will simply have a negative sign to indicate the direction of motion.

5. How does the speed of rotation affect the kinetic energy of a cylinder?

The speed of rotation, or angular velocity, has a direct relationship with the kinetic energy of a rotated cylinder. As the angular velocity increases, so does the kinetic energy, and vice versa.

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