Question

# A barbell spins around a pivot at its center at A. The barbell consists of two...

A barbell spins around a pivot at its center at A. The barbell consists of two small balls, each with mass 450 grams (0.45 kg), at the ends of a very low mass rod of length d = 50 cm (0.5 m; the radius of rotation is 0.25 m). The barbell spins clockwise with angular speed 120 radians/s.

We can calculate the angular momentum and kinetic energy of this object in two different ways, by treating the object as two separate balls, or as one barbell.

I: Treat the object as two separate balls

(a) What is the speed of ball 1?
|| = m/s

(b) Calculate the translational angular momentum trans, 1, A of just one of the balls (ball 1).
|trans, 1, A| = kg Â· m2/s
zero magnitude; no direction into page     out of page

(c) Calculate the translational angular momentum trans, 2, A of the other ball (ball 2).
|trans, 2, A| = kg Â· m2/s
out of pagezero magnitude; no direction     into page

(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, tot, A.
|tot, A| = kg Â· m2/s
out of pagezero magnitude; no direction     into page

(e) Calculate the translational kinetic energy of ball 1.
Ktrans,1 =
 1 2
m||2
= J

(f) Calculate the translational kinetic energy of ball 2.
Ktrans,2 =
 1 2
m||2
= J

(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.
Ktotal = J

II: Treat the object as one barbell

(h) Calculate the moment of inertia I of the barbell.
I = kg Â· m2
(i) What is the direction of the angular velocity vector ?
zero magnitude; no direction out of page     into page

(j) Use the moment of inertia I and the angular speed || = 120 rad/s to calculate the rotational angular momentum of the barbell:
|rot| = I || = kg Â· m2/s
zero magnitude; no direction out of page     into page

(k) How does this value, |rot|, compare to the angular momentum |tot, A| calculated earlier by adding the translational angular momenta of the two balls?
|rot| > |tot, A||rot| = |tot, A|    |rot| < |tot, A|

(l) Use the moment of inertia I and the angular speed || = 120 rad/s to calculate the rotational kinetic energy of the barbell:
Krot =
 1 2
Iω2
= J
(m) How does this value, Krot, compare to the kinetic energy Ktotal calculated earlier by adding the translational kinetic energies of the two balls?
Krot > KtotalKrot < Ktotal    Krot = Ktotal

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