Question:A barbell spins around a pivot at its center at
A.
The barbell consists of two...
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· m^{2}/s
zero magnitude;
no directioninto
page out of
page
(c) Calculate the
translational
angular momentum_{trans,
2, A}
of the other ball (ball 2).
|_{trans,
2, A}|
=
kg Â· m^{2}/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· m^{2}/s
out of
pagezero magnitude;
no direction into
page
(e) Calculate the
translational
kinetic energy of ball 1.
K_{trans,1}
=
1
2
m||^{2}
=
J
(f) Calculate the
translational
kinetic energy of ball 2.
K_{trans,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.
K_{total}
=
J
II: Treat the object as one barbell
(h) Calculate the moment of inertia
I
of the barbell.
I
=
kg Â· m^{2}
(i) What is the direction of the angular velocity vector
?
zero magnitude;
no directionout 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· m^{2}/s
zero magnitude;
no directionout 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?
(l) Use the moment of inertia
I
and the angular speed ||
= 120
rad/s to calculate the rotational kinetic energy of the
barbell:
K_{rot}
=
1
2
Iω^{2}
=
J
(m) How does this value,
K_{rot},
compare to the kinetic energy
K_{total}
calculated earlier by adding the translational kinetic energies of
the two balls?