A 1 kg mass and a 6 kg mass are attached to either end of a 3 m long massless ro

Question

A 1 kg mass and a 6 kg mass are attached to either end of a 3 m long massless rod.

a.) Find the center of mass of the system.
___m, from the 1 kg mass.

Find the rotational inertia (I) of the system when rotated about:
b.) the end with the 1 kg mass.
___kg m2
c.) the end with the 6 kg mass.
___kg m2
d.) the center of the rod.
___kg m2
e.) the center of mass of the system.
___kg m2
(Compare this to parts b-d. Is this what you expect?)

f.) If the system is rotated about the center of mass by a force of 10 N acting on the 6 kg mass, (perpendicular to the rod), what will the size of the angular acceleration of the system be?
___rad/s2

Explanation / Answer

set 0 at the 1 kg mass. (0*1+6*3)/7 18/7 meters from it. b. I=m2*L^2 = 6*3^2 =54 kg·m^2 c. I=m1*L^2 = 1*3^2 =9 kg·m^2 d. I=m1*(L/2)^2 + m2*(L/2)^2 = (1+6)*(3/2)^2 =15.75 kg·m^2 e. I=m1*x1^2 + m2*x2^2 = 1*18/7^2 + 6*(3-18/7)^2 =7.71 yes, it should be the smallest of them. T=I*w’ T=F*x2, F=10N, x2=L-x1=(3-18/7)=0.428 w’=T/I = 10*0.428/7.71=0.555

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