A hoop of radius R is made to rotate at constant angular speed @ around a diameter, as shown in Fig. 10.20. A small bug of mass m walks at constant angular speed 2 around the hoop. Let F be the total force that the hoop applies to the bug when the bug is at the angle shown, and let F₁ be the component of F that is perpendicular to the plane of the hoop. Find F₁ in two ways (ignore gravity in this problem): (a) Work in the lab frame: At the angle 0, find the rate of change of the bug's angular momentum around the rotation axis, and then consider the torque on the bug. (b) Work in the rotating frame of the hoop: At the angle , find the Fig. 10.20 relevant fictitious force, and then take it from there. bug 10
A hoop of radius R is made to rotate at constant angular speed @ around a diameter, as shown in Fig. 10.20. A small bug of mass m walks at constant angular speed 2 around the hoop. Let F be the total force that the hoop applies to the bug when the bug is at the angle shown, and let F₁ be the component of F that is perpendicular to the plane of the hoop. Find F₁ in two ways (ignore gravity in this problem): (a) Work in the lab frame: At the angle 0, find the rate of change of the bug's angular momentum around the rotation axis, and then consider the torque on the bug. (b) Work in the rotating frame of the hoop: At the angle , find the Fig. 10.20 relevant fictitious force, and then take it from there. bug 10
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10.22. Bug on a hoop **
A hoop of radius R is made to rotate at constant angular speed @ around
a diameter, as shown in Fig. 10.20. A small bug of mass m walks at
constant angular speed around the hoop. Let F be the total force that
the hoop applies to the bug when the bug is at the angle shown, and
let F be the component of F that is perpendicular to the plane of the
hoop. Find F₁ in two ways (ignore gravity in this problem):
0
(a) Work in the lab frame: At the angle 0, find the rate of change of
the bug's angular momentum around the rotation axis, and then
consider the torque on the bug.
(b) Work in the rotating frame of the hoop: At the angle 0, find the Fig. 10.20
relevant fictitious force, and then take it from there.
R
-bug
18
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