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 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.)

(d) Find the linear acceleration of the particle labeled 3 at t = 0.

(e) Find the maximum kinetic energy of the system.
Kf =

(f) Find the maximum angular speed attained by the rod.
?f =

(g) Find the maximum angular momentum of the system.
Lf =

(h) Find the maximum speed attained by the particle labeled 2.
vf =

Explanation / Answer

Ip = md²[(1/3)²+(4/3)²+(2/3)²] = (7/3)md² From E = ½Ip*w² we get 1) w = v[2E/I] You already have E = mgd; substituting in (1), w = v[(6/7)(g/d)] V2 = w*R2 = w*d/3 = (1/3)v[6gd/7]

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