In the figure below,a disk (radius R = 1.0 m,mass = 2.0 kg)is suspended from a pivot a distance d = 0.25 m above its center of mass.For a circular disk,
)The angular frequency (in rad/s)for small oscillations is approximately
A)4.2
B)2.1
C)1.5
D)1.0
E)3.8

Question

In the figure below,a disk (radius R = 1.0 m,mass = 2.0 kg)is suspended from a pivot a distance d = 0.25 m above its center of mass.For a circular disk, 
)The angular frequency (in rad/s)for small oscillations is approximately 
A)4.2 
B)2.1 
C)1.5 
D)1.0 
E)3.8

Quizplus · Accepted Answer

The angular frequency (ω) for small oscillations of a simple pendulum is given by the equation:
ω = √(g/L)
where g is the acceleration due to gravity (9.81 m/s²) and L is the length of the pendulum. 
For this disk, the effective length of the pendulum is d + R/2 = 0.25 + 0.5 = 0.75 m (assuming small oscillations). 
So, ω = √(g/L) = √(9.81/0.75) = 2.077 rad/s (approx. 2.1 rad/s). 
Therefore, the best choice is B) 2.1.

In the Figure Below,a Disk (Radius R = 1