All Problems

Laws of Conservation

Problem 1.142

A smooth light horizontal rod \(A B\) can rotate about a vertical axis passing through its end \(A\). The rod is fitted with a small sleeve of mass \(m\) attached to the end \(A\) by a weightless spring of length \(l_{0}\) and stiffness \(x .\) What work must be performed to slowly get this system going and reaching the angular velocity \omega?

Reveal Answer
A=xl02η(1+η)/2(1−η)2, where η=mω2/xA=x l_{0}^{2} \eta(1+\eta) / 2(1-\eta)^{2}, \text { where } \eta=m \omega^{2} / x
Prev
Next