9.46. Slightly wobbling * A coin of mass m and radius R is initially spinning around...

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9.46. Slightly wobbling * A coin of mass m and radius R is initially spinning around the axis perpendicular to its plane, with angular speed w3. It is supported by a pivot at its center. You apply an infinitesimal downward strike at a point on the rim, as shown in Fig. 9.63, giving the coin an infinitesimal angular velocity component @_ in the plane of the coin. When the plane of the coin returns to its original plane for the first time, what (approximately) is the orientation of the coin? 9.47. Original orientation ** A coin of mass m and radius R is initially spinning around the axis per- pendicular to its plane, with angular speed w3. It is supported by a pivot at its center. You apply a (nonzero) downward strike at a point on the rim, as shown in Fig. 9.63, giving the coin an angular velocity com- ponent w in the plane of the coin. Consider the nth time the plane of the coin returns to its original plane. What is the minimum value of n for which it is possible for the coin to have exactly the same orienta- tion as when it started? What should @_ be in terms of w3 to achieve this? Fig. 9.63 W3 F 9.46. Slightly wobbling * A coin of mass m and radius R is initially spinning around the axis perpendicular to its plane, with angular speed w3. It is supported by a pivot at its center. You apply an infinitesimal downward strike at a point on the rim, as shown in Fig. 9.63, giving the coin an infinitesimal angular velocity component @_ in the plane of the coin. When the plane of the coin returns to its original plane for the first time, what (approximately) is the orientation of the coin? 9.47. Original orientation ** A coin of mass m and radius R is initially spinning around the axis per- pendicular to its plane, with angular speed w3. It is supported by a pivot at its center. You apply a (nonzero) downward strike at a point on the rim, as shown in Fig. 9.63, giving the coin an angular velocity com- ponent w in the plane of the coin. Consider the nth time the plane of the coin returns to its original plane. What is the minimum value of n for which it is possible for the coin to have exactly the same orienta- tion as when it started? What should @_ be in terms of w3 to achieve this? Fig. 9.63 W3 F