Question

Rigid rods of negligible mass lying along the y axis connect three particles. The system rotates about the x axis with an angular speed of 4.00 rad/s. (The center of mass of mass m1 = 6.20 kg is at location yl = 4.65 m, the center of mass of m2 = 3.10 kg is at y2 = -3.10 m, and the center of mass of m2 = 4.65 kg is at y3 = -6.20 m.)

Answer 1

a) I = I1 + I2 + I3

= 6.2*4.65^2 + 3.1*3.1^2 + 4.65*6.2^2

= 342.6 kg.m^2

b) KE(rotational) = 0.5*I*w^2

= 0.5*342.6*4^2

= 2740.8 J

c)

v1 = 4.65*4 = 18.6 m/s

v2 = 3.1*4 = 12.4 m/s

v3 = 6.2*4 = 24.8 m/s

d) total KE = 0.5*m1*v1^2 + 0.5*m2*v2^2 + 0.5*m3*v3^2

= 0.5*6.2*18.6^2 + 0.5*3.1*12.4^2 + 0.5*4.65*24.8^2

= 2740.8 J

e) 3rd option is corrrect answer

net 0.5*m*vi^2 = 0.5*I*w^2