A rigid, massless rod has three particles with equal masses attached to it as sh

Question

A rigid, massless rod has three particles with equal masses attached to it as shown in the figure below. The rod is free to rotate in a vertical plane about a frictionless axle perpendicular to the rod through the point P and is released from rest in the horizontal position at t = 0. Assume that m and d are known. (Use the following as necessary: m, d, and g.) (a) Find the moment of inertia of the system (rod plus particles) about the pivot. IP = (b) Find the torque acting on the system at t = 0. ?P = counterclockwise (c) Find the angular acceleration of the system at t = 0. ? = counterclockwise (d) Find the linear acceleration of the particle labeled 3 at t = 0. a = upward (e) Find the maximum kinetic energy of the system. KEmax = (f) Find the maximum angular speed reached by the rod. ?max = (g) Find the maximum angular momentum of the system. Lmax = (h) Find the maximum translational speed reached by the particle labeled 2. v2 max =

Explanation / Answer

a) treatinq the masses as point masses
I=m*d^2*(16/9+1/9+4/9)
simplify

I=m*d^2*7/3

f) using energy
m*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 algebra

sqrt(3*g/(7*d))=

g) I*

sqrt(7*g/3)*m*d

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