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.
A body moves from:position (1.0 m)i− (3.0 m)j where its velocity is (2.0 m/s)i+ (0.5 m/s)jto position (−1.0 m)i+ (1.0 m)j where its velocity is (4.0m/s)iExpress the body’s displacement (vector) delta r.Express the body’s change in velocity (vector) delta v.
A particle undergoes three consecutive displacements: AT, = (15î + 30j + 12k) cm, Af, = (23 î – 14j – 5.0k) cm, and
AT, = (-13î+ 15j) cm. Find unit-vector notation for the resultant displacement and its magnitude.
The velocity v→ of a particle moving in the xy plane is given by v→=(5.50t-5.00t2)î+9.00ĵ, with v→ in meters per second and t (> 0) in seconds. At t = 1.40 s and in unit-vector notation, what are (a) the x component and (b) the y component of the acceleration? (c) When (if ever) is the acceleration zero? (d) At what positive time does the speed equal 10.0 m/s?
Physics for Scientists and Engineers with Modern Physics
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.