The figure above represents a stick of uniform density that is attached to a pivot at the right end and has equally spaced marks
along its length. Any one or a combination of the four forces shown can be exerted on the stick as indicated. All four forces are exerted on the stick that is initially at rest. What is the angular momentum of the stick after 2.0s ?
1 answer:
Answer:
After a duration of 2.0 seconds, the angular momentum of the system is .
Explanation:
Let’s denote the forces acting on the rod as A, B, C, and D, and the distance between them as .
The torque produced by force A can be expressed as
,
for force B the torque is
,
the torque for force C is
,
and the torque due to force D is
.
This leads to a total torque on the stick as
Subsequently, this torque results in an angular acceleration in accordance with the formula
where represents the moment of inertia of the stick, which has a value of
.
Thus, the angular acceleration calculates to
.
Now, the angular momentum of the rod is given by
,
where is considered the angular velocity.
Given , we conclude that
Thus, , the angular momentum is
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Answer:
θ = 61.3°
Alicia must swim at an angle of 61.3°
Explanation:
Parameters given include:
Width of the river = 100 m
Alicia's speed in still water = 2.5 m/s
Speed of river's current = 1.2 m/s
The angle she needs to swim can be determined by combining the velocities, taking into account the current's influence.
Her swimming speed aimed against the current must offset the current's velocity;
2.5cosθ - 1.2 = 0
2.5cosθ = 1.2
cosθ = 1.2/2.5
θ = cosinverse(1.2/2.5)
θ = 61.3°
We will use the equations of rotational kinematics,
(A)
(B)
Here, and
denote the final and initial angular displacements, respectively, whereas
and
represent final and initial angular velocities, and
is the angular acceleration.
We are provided with and
.
By substituting these values into equation (A), we have
Now, using equation (B),
This indicates that the wheel's angular speed at the 4.20-second mark is 36.7 rad/s.