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 system can be found using the parallel axis theorem:
$I = \frac{1}{12}ML^2 + M\left(\frac{L}{2}ight)^2 = \frac{13}{48}ML^2$
The kinetic energy can be found using:
$K = \frac{1}{2}I\omega^2 = \frac{1}{2} \cdot \frac{13}{48}ML^2 \cdot (5.0 	ext{ rad/s})^2 = 12 	ext{ J}$

The Rigid Body Shown Rotates About an Axis Through Its