An object of mass M = 3.00kg is attached to a spring with spring constant k = 82

Question

An object of mass M = 3.00kg is attached to a spring with spring constant k = 825N/m whose unstretched length is L = 0.190m , 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.

1-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.

2-Assume that, at a certain angular speed w2, the radius R becomes twice L. Find w2.

An object of mass M = 3.00kg is attached to a spring with spring constant k = 825N/m whose unstretched length is L = 0.190m , 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. 1-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. 2-Assume that, at a certain angular speed w2, the radius R becomes twice L. Find w2.

Explanation / Answer

By F = mv^2/r = kx
=>3 x r x (omega)^2 = kx [by v = r x omega]
=>3 x L x 25 = 825 x [L - 0.19]
=>75L = 825L - 156.75
=>750L = 156.75
=>L = 156.75/750 = 0.209 m
this is the radius at which the mass rotates

Use the same formula as part A, but with different values for r and x:
mr?

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