Ahollow sphere of radius 0.200 m, with rotational inertia i = 0.0484 kg·m2 about a line through its center of mass, rolls without slipping up a surface inclined at 27.1° to the horizontal. at a certain initial position, the sphere's total kinetic energy is 20.0 j. (a) how much of this initial kinetic energy is rotational? (b) what is the speed of the center of mass of the sphere at the initial position? when the sphere has moved 0.900 m up the incline from its initial position, what are (c) its total kinetic energy and (d) the speed of its center of mass?

Part a)

Part b)

v = 3.64 m/s

Part c)

Part d)

Explanation:

As we know that moment of inertia of hollow sphere is given as

here we know that

R = 0.200 m

now we have

now we know that total Kinetic energy is given as

Part a)

Now initial rotational kinetic energy is given as

Part b)

speed of the sphere is given as

v = 3.64 m/s

Part c)

By energy conservation of the rolling sphere we can say

Part d)

Now we know that

answer: decibel

explanation:

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.