How does rotational motion contribute to an object's total kinetic energy?

[kaspis245]

Homework Statement

Same mass sphere and cylinder are rolling on a horizontal plane. Which part of each objects kinetic energy does objects rotational energy make up?

Homework Equations

E_rotational = 1/2 Iw²

E_kinetic = 1/2 mv²

The Attempt at a Solution

[/B]
I know, that moments of inertia are:

I_cylinder = 1/2 MR²

I_sphere = 2/5 MR²

And I know that:

E_total = E_k + E_rotational

What sould I do?

 

[Doc Al]

What sould I do?

For rolling without slipping, how are $\omega$ and $v$ related?

 

[kaspis245]

Well, v = wR .

 

[Doc Al]

Well, v = wR .

Exactly. Use that to relate rotational and translational kinetic energy.

 

[HalfLostAndSearching]

Rotational motion contributes to an object's total kinetic energy by adding energy due to the object's rotation about its axis. This is represented by the equation Erotational = 1/2 Iw^2, where I is the moment of inertia and w is the angular velocity. This rotational energy adds to the object's linear kinetic energy, which is represented by the equation Ekinetic = 1/2 mv^2, where m is the mass of the object and v is the linear velocity.

In the case of a sphere and a cylinder rolling on a horizontal plane, the rotational energy makes up a significant portion of the object's total kinetic energy. This is because both objects have a non-zero moment of inertia, which means they have the ability to rotate and thus contribute to their total kinetic energy.

To calculate the exact portion of kinetic energy due to rotation, we can use the equation Etotal = Ek + Erotational. For a sphere, the moment of inertia is 2/5 MR^2, so the rotational energy would make up 2/5 of the total kinetic energy. For a cylinder, the moment of inertia is 1/2 MR^2, so the rotational energy would make up 1/2 of the total kinetic energy.

In summary, rotational motion contributes to an object's total kinetic energy by adding energy due to rotation about its axis. In the case of a sphere and a cylinder rolling on a horizontal plane, the rotational energy makes up a significant portion of the object's total kinetic energy.