In this problem, we are required to explain the behaviour of springs.

A spring extends linearly until it reaches its elastic limit.

An object of mass M is attached to a spring with spring constant k whose unstretched length is L, and whose far end is fixed to a shaft that is rotating with angular speed ω. Neglect gravity and assume that the mass rotates with angular speed omega as shown. (Figure 1) When solving this problem use an inertial coordinate system, as drawn here. (Figure 2)

What is happening to the spring as the angular velocity approaches ω_{crit}?

A. The spring stretches linearly then breaks at ω = ω_{crit}.

B. The value of ω_{crit} is so large that the spring will behave linearly for any practically attainable ω.

C. As ω_{c} approaches ω_{crit} the spring stops behaving linearly and begins to act more like an unstretchable rod until it eventually breaks.

Frequently Asked Questions

What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Rotational Velocity & Acceleration concept. You can view video lessons to learn Rotational Velocity & Acceleration. Or if you need more Rotational Velocity & Acceleration practice, you can also practice Rotational Velocity & Acceleration practice problems.

What professor is this problem relevant for?

Based on our data, we think this problem is relevant for Professor Taffard's class at UCI.