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.
Ï„P = counterclockwise

(c) Find the angular acceleration of the system at t = 0.
α = 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.
ωmax =

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

(h) Find the maximum translational speed reached by the particle labeled 2.

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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