Answer:
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.
