The rigid body shown rotates about an axis through its centre 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 centre 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 by the formula K = (1/2)Iω^2, where I is the moment of inertia and ω is the angular velocity. Since the object is treated as a particle, its moment of inertia would be I = ML^2/12 (for a rod rotating about its centre of mass). Substituting the given values, we get I = (2.0 kg)(0.8 m)^2/12 = 0.107 kg⋅m^2. Substituting this and the given angular speed of ω = 5.0 rad/s into the formula for K, we get K = (1/2)(0.107 kg⋅m^2)(5.0 rad/s)^2 = 12 J. Therefore, the correct answer is C) 12 J.

The Rigid Body Shown Rotates About an Axis Through Its