Asolid sphere of radius r, a solid cylinder of radius r, and a hollow cylinder of radius r all have the same mass, and all three are rotating with the same angular velocity. the sphere is rotating around an axis through its center, and each cylinder is rotating around its symmetry axis. which one has the greatest rotational kinetic energy?

(a) both cylinders have the same rotational kinetic energy
(b) the solid cylinder
(c) the solid sphere
(d) they all have the same rotational kinetic energy
(e) the hollow cylinder

A)

Explanation: In order to explain this problem we have to consider the kinetic energy of rotation  for rigid body which is given by:

Ekr=1/2*I*ω^2 where I and w are the inertia mometum and angular velocity, respectively.

Also we know that the radius and mass are the same for all rigid bodies. The inertia momentum for the  hollow and solid cylinder  around its symmetry axis, is equal to:

1/2 m*R^2.

The inertia momentum for the sphere, around an axis through its center, is: 2/5*m*R^2 ;

then the greatest rotational kinetic energy is for the cylinders.

(D) they all have the same rotational kinetic energy

Explanation:

Since they all have the same mass and with same angular velocity, the formula is 1/2Iω2

Where w is angular velocity and l is moment of inertia, so since all of the values of the formula are equal in all of the options, you do not actually have any difference between the cylinders and the sphere, so they all have the same rotational kinetic energy.

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