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.
6.00k, with t in seconds and r in meters.
An electron's position is given by 7 = 4.00tî – 5.00t2 ĵ +
(a) In unit-vector notation, what is the electron's velocity v (t)? (Use the following as necessary: t.)
V (t) =
m/s
(b) What is v in unit-vector notation at t = 5.00 s?
v(t = 5.00) =
m/s
(c) What is the magnitude of v at t = 5.00 s?
m/s
(d) What angle does v make with the positive direction of the x axis at t = 5.00 s?
° (from the +x axis)
A particle undergoes three consecutive displacements d1=(1.5i+3.0j-1.2km) cm, d2=(2.3i-1.4j-3.6k) cm and d3=(-1.3i+1.5j) cm. find the component and its magnitude.
Physics for Scientists and Engineers: A Strategic Approach, Vol. 1 (Chs 1-21) (4th Edition)
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