At the instant the displacement of a 2.00 kg object relative to the origin is d → = ( 2.00 m ) i ^ + ( 4 .00 m ) j ^ − ( 3.00 m ) k ^ , its velocity is v → = − ( 6.00 m/s ) i ^ + ( 3 .00 m/s ) j ^ + ( 3.00 m/s ) k ^ and it is subject to a force F → = ( 6.00 N ) i ^ − ( 8 .00 N ) j ^ + ( 4.00 N ) k ^ . Find (a) the acceleration of the object, (b) the angular momentum of the object about the origin, (c) the torque about the origin acting on the object, and (d) the angle between the velocity of the object and the force acting on the object.
At the instant the displacement of a 2.00 kg object relative to the origin is d → = ( 2.00 m ) i ^ + ( 4 .00 m ) j ^ − ( 3.00 m ) k ^ , its velocity is v → = − ( 6.00 m/s ) i ^ + ( 3 .00 m/s ) j ^ + ( 3.00 m/s ) k ^ and it is subject to a force F → = ( 6.00 N ) i ^ − ( 8 .00 N ) j ^ + ( 4.00 N ) k ^ . Find (a) the acceleration of the object, (b) the angular momentum of the object about the origin, (c) the torque about the origin acting on the object, and (d) the angle between the velocity of the object and the force acting on the object.
At the instant the displacement of a 2.00 kg object relative to the origin is
d
→
=
(
2.00
m
)
i
^
+
(
4
.00 m
)
j
^
−
(
3.00
m
)
k
^
, its velocity is
v
→
=
−
(
6.00
m/s
)
i
^
+
(
3
.00 m/s
)
j
^
+
(
3.00
m/s
)
k
^
and it is subject to a force
F
→
=
(
6.00
N
)
i
^
−
(
8
.00 N
)
j
^
+
(
4.00
N
)
k
^
. Find (a) the acceleration of the object, (b) the angular momentum of the object about the origin, (c) the torque about the origin acting on the object, and (d) the angle between the velocity of the object and the force acting on the object.
Definition Definition Product of the moment of inertia and angular velocity of the rotating body: (L) = Iω Angular momentum is a vector quantity, and it has both magnitude and direction. The magnitude of angular momentum is represented by the length of the vector, and the direction is the same as the direction of angular velocity.
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Checkpoint 4
The figure shows four orientations of an electric di-
pole in an external electric field. Rank the orienta-
tions according to (a) the magnitude of the torque
on the dipole and (b) the potential energy of the di-
pole, greatest first.
(1)
(2)
E
(4)
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