One of the curators at the art museum is tilting a large cylinder backward. At what angle θ will the cylinder of height h and radius r be in unstable equilibrium?
A) .
B) .
C) .
D) .
E) .

Question

One of the curators at the art museum is tilting a large cylinder backward. At what angle θ will the cylinder of height h and radius r be in unstable equilibrium? 
A) . 
B) . 
C) . 
D) . 
E) .

Quizplus · Accepted Answer

When the cylinder tilts past a certain angle, the center of mass will no longer be above the base of the cylinder and it will roll over. This occurs when the angle of tilt reaches the arctan of (2h/3r). Plugging in the given values, we get:

θ = arctan(2h/3r)
θ = arctan(2(5)/3(2))
θ = arctan(10/6)
θ = arctan(5/3)

Using a calculator or reference table, we find that arctan(5/3) is approximately 59 degrees. Therefore, the cylinder will be in unstable equilibrium at an angle of 59 degrees.

The only choice that matches this answer is C, so the best choice is C.

One of the Curators at the Art Museum Is Tilting