The rigid object shown is rotated about an
axis perpendicular to the paper and through
center point O. The total kinetic energy of
the object as it rotates is 8 J.

a) What is the moment of inertia of the ob-
ject? Neglect the mass of the connecting rods
and treat the masses as point masses.
Answer in units of kg · m2

b)What is the angular velocity of the object?
Answer in units of rad/s

Since the object is rotating, it will have a Rotational Kinetic Energy and Angular Velocity, that can be related by the equation below:

K.E= ½Iω2.

Defined as

Rotational kinetic energy = ½ moment of inertia * (angular speed)2..

K.E = 8J.

Therefore, making the moment of inertia, I the subject of the relation, we have

2*K.E = I * (Angular Velocity)2

Divide both sides by (Angular Velocity)2 and putting K.E = 8J,

(a) I = (2 x 8)/(Angular Velocity)2

I = 16/(ω2) Kg.m2

(b) Angular Velocity ω is calculated by making ω the subject of the relation

ω2 = (2 *K.E)/I

ω2 = (2 x 8)I = 16/I

Taking square root of both sides

ω = Sqrt(16/I) = 4/Sqrt(I) rad/s

Explanation:

When an object is rotating about its center of mass, its rotational kinetic energy is K = ½Iω2.

Rotational kinetic energy = ½ moment of inertia * (angular speed)2.

When the angular velocity of a spinning wheel doubles, its kinetic energy increases by a factor of four.

When an object has translational as well as rotational motion, we can look at the motion of the center of mass and the motion about the center of mass separately. The total kinetic energy is the sum of the translational kinetic energy of the center of mass (CM) and the rotational kinetic energy about the CM, Which is center O in the question.

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.

490 n

f=125n a=2.5m/s2