Rotational Velocity & Acceleration Video Lessons

Concept

Problem: An object of mass M = 5.00 kg is attached to a spring with spring constant k = 220 N/m whose unstretched length is L = 0.180 m , and whose far end is fixed to a shaft that is rotating with an angular speed of ω = 2.00 radians/s . Neglect gravity and assume that the mass also rotates with an angular speed of 2.00 radians/sGiven the angular speed of  ω = 2.00 radians/s , find the radius R(ω) at which the mass rotates without moving toward or away from the origin, in meters.

FREE Expert Solution

Spring force:

$\overline{){\mathbf{F}}{\mathbf{=}}{\mathbf{k}}{\mathbf{x}}}$

Centripetal force:

$\overline{){\mathbf{F}}{\mathbf{=}}\frac{\mathbf{m}{\mathbf{v}}^{\mathbf{2}}}{\mathbf{r}}{\mathbf{=}}{\mathbf{m}}{\mathbf{r}}{{\mathbf{\omega }}}^{{\mathbf{2}}}}$

(a)

ΣF = mRω2 - kx = 0

mRω2 = kx

mRω2 = k(R - L)

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Problem Details

An object of mass M = 5.00 kg is attached to a spring with spring constant k = 220 N/m whose unstretched length is L = 0.180 m , and whose far end is fixed to a shaft that is rotating with an angular speed of ω = 2.00 radians/s . Neglect gravity and assume that the mass also rotates with an angular speed of 2.00 radians/s

Given the angular speed of  ω = 2.00 radians/s , find the radius R(ω) at which the mass rotates without moving toward or away from the origin, in meters.