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A Rotating Rod: A rigid, massless rod has three particles with equal mass attach

ID: 2093190 • Letter: A

Question


A Rotating Rod:




A rigid, massless rod has three particles with equal mass attached to it in thepositions shown in the diagram. The rod is free to rotate in a vertical plane about a frictionless axleperpendicular to the rod through the point P. It is released from rest at the horizontal position shown attime t = 0. Assuming that m and d are known quantities, find:


(a) the moment of inertia of the system,

(b) the torque acting on the system at t = 0,

(c) the angular acceleration of the system, and the linear acceleration of particle number 3 at t =0,

(d) the maximum kinetic energy of the system, and

(e) the maximum angular momentum of the system.


Explanation / Answer

a) treatinq the masses as point massesI=m*d^2*(16/9+1/9+4/9) simplifyI=m*d^2*7/3f) using energym*g*d*(1/6+4/6-2/6) =.5*I*?^2 solve for ?m*g*d*(1/6+4/6-2/6) =.5*m*d^2*21*?^2/9 do some algebrasqrt (3*g/(7*d))=?g) I*?sqrt(7*g/3)*m*d... Ip = md