A 2.00-m-long 6.00-kg ladder pivoted at the top hangs down from a platform at the circus. A 42.0-kg trapeze artist climbs to a point where her center of mass is at the center of the ladder and swings at the system's natural frequency. The angular frequency (in s−1) of the system of ladder and woman is
A)1.01.
B)3.07.
C)4.03.
D)8.05.
E)16.2.

Question

Quizplus · Accepted Answer

The system's natural frequency can be calculated using the formula for the angular frequency of a physical pendulum: ω = sqrt(g / L_eff), where L_eff is the effective length of the pendulum. The center of mass of the system is at the midpoint of the ladder, so L_eff = 1.00 m. Using g = 9.81 m/s², ω = sqrt(9.81 / 1.00) ≈ 3.13 s⁻¹, which is closest to 3.07 s⁻¹.

A 200-M-Long 6