No. Radius of gyration depends upon the axis of rotation of the body.

One formula to calculate centripetal acceleration is:

a = omega2r, where omega is the angular velocity.

Combining this with Newton's Second Law:

F=ma

you get:

F = m omega2 r

For completeness sake, omega (in radians per second) = 2 pi f (2 x pi x the frequency,

in revolutions / second). Thus, omega and the frequency are proportional.

As you can see, the force is proportional to the square of the angular velocity.

For example, doubling the frequency would cause double the angular velocity,

which would require an increase of the force by a factor of 4.

The rotating object's moment of inertia.

Similar to Newton's Second Law, commonly quoted as "force = mass x acceleration", there is an equivalent law for rotational movement: "torque = moment of inertia x angular acceleration". The moment of inertia depends on the rotating object's mass and its exact shape - you can even have a different moment of inertia for the same shape, if the axis of rotation is changed. If you use SI units, and radians for angles (and therefore radians/second2 for angular acceleration), no further constants of proportionality are required.

Yes. According to Newton's Second Law, there has to be an unbalanced force - otherwise, the satellite won't accelerate (in this case, change direction).

velosity in circular path angular

Assuming that angles are measured in radians, and angular velocity in radians per second (this simplifies formulae):

Radius of rotation is unrelated to angular velocity.

Linear velocity = angular velocity x radius

Centripetal acceleration = velocity squared / radius

Centripetal acceleration = (angular velocity) squared x radius

Centripetal force = mass x acceleration = mass x (angular velocity) squared x radius

Because there is no centrifugal force. The force of circular motion is inward, thus centripetal. If you are on a car that makes a quick right turn, you feel a "centrifugal" force leftward. But in reality, it is the car making an acceleration to the center of the curve, which is to your right. What you feel is inertia, not a force.

Clockwise, top rotating to the right, and counterclockwise, top rotating to the left is only a perspective based on the position of the observer. The torque is the rotational force of the rotating object. Most often the perspective of the observer is from the driving end of a shaft facing the driven machine. The amount of torque at a given speed of the driving machine (engine or motor) is mechanically converted into work by the driven machine (generator, pump, compressor...etc.).

An quarter turn

No, they aren't the same. Revolution is the object moving in a circular motion. Rotation is when the object stays in one place and spins around.

Without knowing the angular speed, i.e. RPM or some such velocity, it is not possible to answer the question. Please restate the question, giving all of the required information.

Because of energy loss via friction.

If they are both solid, and the incline is the same, the rate of acceleration will be the same.