The question is based on Rotational Mechanics. Find the correct option (s)?

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Amelia Adams · Accepted Answer

See below.

We've got #l=sqrt(24)a# #l_g=l+1/5 l = 6/5l# #vec r_g = (0,l_g/cosalpha,0)# where #(u,v,w)# must be understood as #u hat i + v hat j + w hat k# Here #alpha = arctan(1/sqrt(24))# #vec omega = (0,cosalpha,sinalpha)omega# #vec v_g = vec r_g xx vec omega = 17/2a^2m omega(0,cosalpha,sinalpha)# then #abs(vec v_g)=17/2a^2m omega# additionally (D) #Omega = abs(vec v_g)/abs(vec r_g) = 1/5 a omega# or #vec Omega = (0,0,1)Omega# Right now #vec L_O = J_(omega) vec omega+J_(Omega) vec Omega# along with #J_(omega)=(ma^2)/2+(4m(2a)^2)/2# Additionally, we have #vec L_g = J_(omega) vec omega# and (B) #norm(vec L_g)=17/2a^2m omega# additionally #J_(Omega)=(ma^2)/4+ml_0^2+((4m)(2a)^2)/4+4m(2l_0)^2# with #l_0 = l cos alpha# thus (A) #<< vec L_O, hat k >> = J_(Omega)Omega+J_(omega)<< vec omega, hat k >> = J_(Omega)Omega+J_(omega)omega sin alpha# additionally #norm(vec L_O) = sqrt(<< vec L_O, hat k >>^2+(J_(omega)omega cosalpha)^2 )# or (C) #norm(vec L_O) = sqrt((J_(Omega)Omega)^2+2J_(Omega)J_(omega) Omega omega sinalpha+(J_(omega)omega)^2)# The reader is left with the final numerical results as an exercise.

Carson Alexander · Answer

undefined Sure, I'm ready to help. What's the question or the options you need assistance with in Rotational Mechanics?