An object of mass M = 2.00kg is attached to a spring with spring constant k = 55

Question

An object of mass M = 2.00kg is attached to a spring with spring constant k = 550N/m whose unstretched length is L = 0.110m , and whose far end is fixed to a shaft that is rotating with an angular speed of ? = 5.00radians/s . Neglect gravity and assume that the mass also rotates with an angular speed of 5.00radians/s as shown. (Figure 1) When solving this problem use an inertial coordinate system, as drawn here. (Figure 2)Given the angular speed of ? = 5.00radians/s , find the radius R(?) at which the mass rotates without moving toward or away from the origin.

Explanation / Answer

Here , Let the radius is R

then , For balanced motion

Fspring = Fcentripetal

K*(R - L) = mw^2/R

550 *(R - .0110) = 2*5^2/R

R^2 -0.0110R - 0.09091 = 0

solving for R

R = 0.307 m

the radius R is 0.307 m

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