An object of mass M = 4.00 kg is attached to a spring with spring constant k = 1

Question

An object of mass M = 4.00 kg is attached to a spring with spring constant k = 1100 N/m whose unstretched length is L = 0.170 m , and whose far end is fixed to a shaft that is rotating with an angular speed of = 5.00 radians/s . Neglect gravity and assume that the mass also rotates with an angular speed of 5.00 radians/s.

Given the angular speed of = 5.00 radians/s , find the radius R() at which the mass rotates without moving toward or away from the origin.

R=.187 meters

Assume that, at a certain angular speed 2, the radius R becomes twice L. Find2.

Express your answer in radians per second.

Explanation / Answer

Here ,

let the radius is R

Now , as Force = m * w^2 * R

for the spring , F = k * x

m * w^2 * R = k * (R - 0.17)

4 * 5^2 * R = 1100 * (R - 0.17)

solving for R

R = 0.187 m

R = 0.187 m

the radius of turn is 0.187 m

Here ,

for double the radius , R = 2 * 0.187

R = 0.384 m

4 * w^2 * 0.384 = 1100 * (0.384 - 0.17)

w = 12.4 rad/s

the certain angular speed is 12.4 rad/s

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