An object of mass M = 5.00kg is attached to a spring with spring constant k = 88

Question

An object of mass M = 5.00kg is attached to a spring with spring constant k = 880N/m whose unstretched length is L = 0.140m , and whose far end is fixed to a shaft that is rotating with an angular speed of ? = 4.00radians/s . Neglect gravity and assume that the mass also rotates with an angular speed of 4.00radians/s as shown.

Given the angular speed of ? = 4.00radians/s , find the radius R(?) at which the mass rotates without moving toward or away from the origin.   Express your answer in meters.

An object of mass M = 5.00kg is attached to a spring with spring constant k = 880N/m whose unstretched length is L = 0.140m , and whose far end is fixed to a shaft that is rotating with an angular speed of ? = 4.00radians/s . Neglect gravity and assume that the mass also rotates with an angular speed of 4.00radians/s as shown. (Figure 1) When solving this problem use an inertial coordinate system, as drawn here. (Figure 2) Given the angular speed of ? = 4.00radians/s , find the radius R(?) at which the mass rotates without moving toward or away from the origin. Express your answer in meters.

Explanation / Answer

centripital force = mw^2 .R = kx

5 x 4^2 x R = 880 x (R - 0.140)

R = 0.154 m

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