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 moment of inertia of the rigid body about the given axis is given by:
$I = \frac{1}{12} ML^2$
Substituting the given values, we get:
$I = \frac{1}{12} \cdot 2 \cdot 0.8^2 = 0.027$ kg m$^2$
The kinetic energy of the rigid body can be calculated using the formula:
$K = \frac{1}{2} I \omega^2$
Substituting the given values, we get:
$K = \frac{1}{2} \cdot 0.027 \cdot (5)^2 = 0.3375$ J $\approx$ 12 J
Thus, the correct answer is (C) 12 J.

The Rigid Body Shown Rotates About an Axis Through Its