An object of mass M = 1.00kg is attached to a spring with spring constant k = 44

Question

An object of mass M = 1.00kg is attached to a spring with spring constant k = 44.0N/m whose unstretched length is L = 0.180m , and whose far end is fixed to a shaft that is rotating with an angular speed of = 2.00radians/s . Neglect gravity and assume that the mass also rotates with an angular speed of 2.00radians/s as shown. (Figure 1) When solving this problem use an inertial coordinate system, as drawn here

Given the angular speed of ? = 2.00radians/s , find the radius R(?) at which the mass rotates without moving toward or away from the origin.

An object of mass M = 1.00kg is attached to a spring with spring constant k = 44.0N/m whose unstretched length is L = 0.180m , and whose far end is fixed to a shaft that is rotating with an angular speed of = 2.00radians/s . Neglect gravity and assume that the mass also rotates with an angular speed of 2.00radians/s as shown. (Figure 1) When solving this problem use an inertial coordinate system, as drawn here Given the angular speed of ? = 2.00radians/s , find the radius R(?) at which the mass rotates without moving toward or away from the origin.

Explanation / Answer

NOTE: This question was asked before (see Source). I am paraphrasing that answer.

Equate the centripetal force Fc with the tension force in the spring Ft:

Let R be R(omega). Then

Fc = M * w^2 * R

Ft = k (R

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