Question

A bead lies on a frictionless hoop of radius R that rotates around a vertical diameter with constant angular speed ?, as shown in the figure below. Figure 1 (a) What should ? be so that the bead maintains the same position on the hoop, at an angle ? with respect to the vertical? Express you answer in terms of some or all of the following: ?, R and g. (b) Analyzing the answer for Part A, you will find that there is a range of angular speeds, 0 < ? < ?0 for which the fixed angle ? = 0 (meaning that the only balanced position is at the bottom of the hoop). Find the value of ?0. Express you answer in terms of some or all of the following: R and g.

          A bead lies on a frictionless hoop of radius R that rotates around a vertical diameter with constant angular speed ?, as shown in the figure below.

Figure 1

(a) What should ? be so that the bead maintains the same position on the hoop, at an angle ? with respect to the vertical? Express you answer in terms of some or all of the following: ?, R and g.
(b) Analyzing the answer for Part A, you will find that there is a range of angular speeds, 0 < ? < ?0 for which the fixed angle ? = 0 (meaning that the only balanced position is at the bottom of the hoop). Find the value of ?0. Express you answer in terms of some or all of the following: R and g.

A bead lies on a frictionless hoop of radius R that rotates around a vertical diameter with constant angular speed ?, as shown in the figure below.

Figure 1

(a) What should ? be so that the bead maintains the same position on the hoop, at an angle ? with respect to the vertical? Express you answer in terms of some or all of the following: ?, R and g.
(b) Analyzing the answer for Part A, you will find that there is a range of angular speeds, 0 < ? < ?0 for which the fixed angle ? = 0 (meaning that the only balanced position is at the bottom of the hoop). Find the value of ?0. Express you answer in terms of some or all of the following: R and g.

Added by Cameron B.

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