A 2-m long 6 kg ladder pivoted at the top hangs down from a platform at the circus. A 42 kg trapeze artist climbs to a point where her centre of mass is at the centre 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 is determined by the combined moment of inertia of the ladder and the trapeze artist. The ladder's moment of inertia is (1/3)ML^2, and the trapeze artist's is mL^2/4. The total moment of inertia is I = (1/3)(6)(2)^2 + (42)(2)^2/4. The angular frequency is given by ω = sqrt(g/I), where g is the acceleration due to gravity (9.8 m/s^2). Calculating this gives ω ≈ 3.07 s^-1.

A 2-M Long 6 Kg Ladder Pivoted at the Top