In Figure 11.78 a barbell spins around a pivot at its center at A. The barbell consists of two small balls, each with mass 500
grams (0.5 kg), at the ends of a very low mass rod of length d = 20 cm (0.2 m; the radius of rotation is 0.1 m). The barbell
spins clockwise with angular speed 80 radians/s.
I: Treat the object as two separate balls
(a) What is the speed of ball 1?
(b) What are the magnitude and direction of the translational angular momentum of just one of the balls
(ball 1)?
(c) What are the magnitude and direction of the translational angular momentum of the other ball (ball
2)?
(d) By adding the translational angular momentum of ball 1 and the translational angular momentum of ball 2,
calculate the total angular momentum of the barbell, (magnitude and direction).
(e) Calculate the translational kinetic energy of ball 1.
(f) Calculate the translational kinetic energy of ball 2.
(g) By adding the translational kinetic energy of ball 1 and the translational kinetic energy of ball 2, calculate the total
kinetic energy of the barbell.
II: Treat the object as one barbell
(h) Calculate the moment of inertia I of the barbell.
(i) What is the direction of the angular velocity vector ?
(j) Use the moment of inertia I and the angular speed |ω| = 80 rad/s to calculate the rotational angular momentum of
the barbell (magnitude and direction).
(k) How does this value, , compare to the magnitude of the angular momentum calculated earlier, , by
adding the translational angular momenta of the two balls?
(l) Use the moment of inertia I and the angular speed |ω| = 80 rad/s to calculate the rotational kinetic energy of the
barbell:
(m) How does this value, Krot, compare to the kinetic energy Ktotal calculated earlier by adding the translational kinetic
energies of the two balls?