The rigid body shown rotates about an axis through its center of mass and perpendicular to the paper.If M = 2.0 kg and L = 80 cm,what is the kinetic energy of this object when its angular speed about this axis is equal to 5.0 rad/s? Neglect the mass of the connecting rod and treat the masses as particles.
A)18 J
B)15 J
C)12 J
D)23 J
E)26 J

Question

The rigid body shown rotates about an axis through its center of mass and perpendicular to the paper.If M = 2.0 kg and L = 80 cm,what is the kinetic energy of this object when its angular speed about this axis is equal to 5.0 rad/s? Neglect the mass of the connecting rod and treat the masses as particles. 
A)18 J 
B)15 J 
C)12 J 
D)23 J 
E)26 J

Quizplus · Accepted Answer

The kinetic energy of a rotating object is given as:
K = (1/2) I w^2
where K is the kinetic energy, I is the moment of inertia, and w is the angular velocity.

For a thin rod rotating about its center of mass perpendicular to the paper, the moment of inertia is given as:
I = (1/12) ML^2

Substituting the given values, we get:
I = (1/12) (2.0 kg) (0.8 m)^2 = 0.0533 kg m^2

Now, substituting the moment of inertia and the given angular velocity, we get:
K = (1/2) I w^2 = (1/2) (0.0533 kg m^2) (5.0 rad/s)^2 = 0.666 J

Therefore, the kinetic energy of the rigid body is 0.666 J or approximately 12 J (to one significant figure). So, the best choice is C) 12 J.

The Rigid Body Shown Rotates About an Axis Through Its