A thin circular ring of mass M and radius r is rotating about its axis with constant angular velocity ω. Two objects each of mass m are attached gently to the opposite ends of the diameter of the ring. The ring now rotates with angular velocity given by,

Booster class

Mechanics 1

Skill

Understanding the concept of rotational motion

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mdasfaaruddinshareefLv10

3 Aug 2023

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Uttam SaikiaLv10

3 Dec 2020

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An object of mass M is attached to a spring with spring constant k whose unstretched length is L, and whose far end is fixed to a shaft that is rotating with an angular speed of ω. Neglect gravity and assume that the mass also rotates with an angular speed of ω as shown. (Figure 1)When solving this problem use an inertial coordinate system, as drawn here. (Figure 2)

1) Given the angular speed of ω , find the radius R(ω) at which the mass rotates without moving toward or away from the origin.

2) Assume that, at a certain angular speed ω2, the radius R becomes twice L. Find ω2.

Express your answer in radians per second.

3) You probably have noticed that, as you increase ω, there will be a value. ω_crit, for which R(ω) goes to infinity. Find ω_crit.

orangedeer877

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A space station is constructed in the shape of a hollow ring of mass 5.00 × 10⁴ kg. Members of the crew walk on a deck formed by the inner surface of the outer cylindrical wall of the ring, with radius r = 100 m. At rest when constructed, the ring is set rotating about its axis so that the people inside experience an effective free-fall acceleration equal to g. (See Fig. P10.52.) The rotation is achieved by firing two small rockets attached tangentially to opposite points on the rim of the ring. (a) What angular momentum does the space station acquire? (b) For what time interval must the rockets be fired if each exerts a thrust of 125 N?

redserval182

A space station is constructed in the shape of a hollow ring of mass 5.00 ✕ 10⁴. Members of the crew walk on a deck formed by the inner surface of the outer cylindrical wall of the ring, with radius r=100 m. At rest when constructed, the ring is set rotating about its axis so that the people inside experience an effective free-fall acceleration equal to g. The rotation is achieved by firing two small rockets attached tangentially to opposite points on the rim of the ring.