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.

air exerts forces on falling objects near earth’s surface.

explanation:

the term 'free falls' refer to object that are falling towards the earth, in a situation in which gravity is the only force acting on the object.

for an object in free fall, the acceleration is constant (g, the gravitational acceleration), and so the velocity of the object constantly increases.

for objects near earth's surface, there is always another force acting on the object: the resistance due to the air. this force is opposed to the direction of fall of the object, and it is proportional to the velocity of the object, so as the object falls down, this force increases up to a point when it balances the force of gravity, and the object continues its motion at constant velocity (called terminal velocity). since in this case gravity is not the only force acting on the object, we are not in a situation of free fall.

the design of a ski jumping suit involves a trade-off between giving the skiers lift to get higher jumps and ensuring the skier does not face a lot of drag before the jump itself. an expansive suit may to lift the skier higher, but at the same time, it will also increase the air resistance. higher air resistance as the skier goes down the slope limits the speed of the jump. a big suit also increases the risk of losing balance or control, especially if there's a strong gust of wind. while technologically enhanced suits a lot, clothing is not the only factor in a ski jumper’s success. gathering speed while skiing down the slope, ensuring good speed on the ramp, and maintaining good body posture and form in the air all contribute to a ski jumper's success.