A spinning bicycle wheel with a loaded rim (essentially a hoop)is supported by a line at one end of its axle.The radius of the wheel is 0.305 m,and the wheel has a mass of 3.63 kg.It is spinning at 80.0 rad/s,and the center of mass is 15.2 cm from the point of support.The angular velocity of precession is
A)0.0125 rad/s
B)0.0318 rad/s
C)0.200 rad/s
D)0.100 rad/s
E)0.625 rad/s

Question

Quizplus · Accepted Answer

The angular velocity of precession can be calculated using the formula:

ω_p = (mgh)/(Iω)

Where,
m = mass of the wheel (3.63 kg)
g = acceleration due to gravity (9.81 m/s^2)
h = distance of the center of mass from the point of support (15.2 cm = 0.152 m)
I = moment of inertia of the wheel about its axis of rotation (0.5mr^2)
ω = angular velocity of the wheel (80.0 rad/s)

Substituting the values, we get:

ω_p = (3.63 x 9.81 x 0.152)/(0.5 x 3.63 x 0.305^2 x 80.0) = 0.200 rad/s

Therefore, the correct choice is C) 0.200 rad/s.

A Spinning Bicycle Wheel with a Loaded Rim (Essentially a Hoop)is