The rigid object shown is rotated about an axis perpendicular to the paper and through point P.The total kinetic energy of the object as it rotates is equal to 1.4 J.If M = 1.3 kg and L = 0.50 m,what is the angular velocity of the object? Neglect the mass of the connecting rods and treat the masses as particles.
A)1.3 rad/s
B)1.5 rad/s
C)1.7 rad/s
D)1.2 rad/s
E)2.1 rad/s

Question

The rigid object shown is rotated about an axis perpendicular to the paper and through point P.The total kinetic energy of the object as it rotates is equal to 1.4 J.If M = 1.3 kg and L = 0.50 m,what is the angular velocity of the object? Neglect the mass of the connecting rods and treat the masses as particles. 
A)1.3 rad/s 
B)1.5 rad/s 
C)1.7 rad/s 
D)1.2 rad/s 
E)2.1 rad/s

Quizplus · Accepted Answer

The total kinetic energy of the rotating object can be written as:
K = (1/2)Iω^2
where I is the moment of inertia and ω is the angular velocity.
For a rigid object rotating about an axis perpendicular to the plane of the object, the moment of inertia is given by:
I = (1/12)ML^2
Substituting the given values, we get:
I = (1/12)(1.3)(0.5)^2 = 0.0542 kg·m^2
We are also given that the total kinetic energy is 1.4 J, so we can write:
1.4 = (1/2)(0.0542)ω^2
Solving for ω, we get:
ω = √(2(1.4)/(0.0542)) = 1.7 rad/s
Therefore, the correct answer is C).

The Rigid Object Shown Is Rotated About an Axis Perpendicular