An object of mass M = 4.00 kg is attached to a spring with spring constant k = 1100 N/mN/m whose unstretched length is L = 0.150 mm, and whose far end is fixed to a shaft that is rotating with an angular speed of ω (omega) = 5.00 radians/s . Neglect gravity and assume that the mass also rotates with an angular speed of 5.00 radians/s as shown. When solving this problem use an inertial coordinate system, as drawn here.
Given the angular speed of ω (omega) = 5.00 radians/s , find the radius R (omega) at which the mass rotates without moving toward or away from the origin.
The radius at which the mass doesn't move towards or away from the origin is 165 mm. To get to the solution, all we have to find is the radius at which the centripetal force due to the circular motion is equal to the elastic force from the spring. Just use the known formulae for the elastic force and the centripetal force and substitute in the values. When you equate both of them, you can find the R value.