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11 Dec 2019
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. ωcrit, for which R(ω) goes to infinity. Find ωcrit.
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. ωcrit, for which R(ω) goes to infinity. Find ωcrit.
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Supratim PalLv10
11 Oct 2020
