The Moment of Inertia of the Disc is represented by
. (Correct answer: A)
Let suppose that the Disk is a Rigid Body whose mass is uniformly distributed. The Moment of Inertia of the element is equal to the Moment of Inertia of the entire Disk minus the Moment of Inertia of the Hole, that is to say:
(1)
Where:
- Moment of inertia of the Disk.
- Moment of inertia of the Hole.
Then, this formula is expanded as follows:
(1b)
Dimensionally speaking, Mass is directly proportional to the square of the Radius, then we derive the following expression for the Mass removed by the Hole (
):


And the resulting equation is:



The moment of inertia of the Disc is represented by
. (Correct answer: A)
Please see this question related to Moments of Inertia: brainly.com/question/15246709
Answer:
v = -v₀ / 2
Explanation:
For this exercise let's use kinematics relations.
Let's use the initial conditions to find the acceleration of the electron
v² = v₀² - 2a y
when the initial velocity is vo it reaches just the negative plate so v = 0
a = v₀² / 2y
now they tell us that the initial velocity is half
v’² = v₀’² - 2 a y’
v₀ ’= v₀ / 2
at the point where turn v = 0
0 = v₀² /4 - 2 a y '
v₀² /4 = 2 (v₀² / 2y) y’
y = 4 y'
y ’= y / 4
We can see that when the velocity is half, advance only ¼ of the distance between the plates, now let's calculate the velocity if it leaves this position with zero velocity.
v² = v₀² -2a y’
v² = 0 - 2 (v₀² / 2y) y / 4
v² = -v₀² / 4
v = -v₀ / 2
We can see that as the system has no friction, the arrival speed is the same as the exit speed, but with the opposite direction.
Answer:
The resultant velocity of the helicopter is
.
Explanation:
Physically speaking, the resulting velocity of the helicopter (
), measured in meters per second, is equal to the absolute velocity of the wind (
), measured in meters per second, plus the velocity of the helicopter relative to wind (
), also call velocity at still air, measured in meters per second. That is:
(1)
In addition, vectors in rectangular form are defined by the following expression:
(2)
Where:
- Magnitude, measured in meters per second.
- Direction angle, measured in sexagesimal degrees.
Then, (1) is expanded by applying (2):
(3)

If we know that
,
,
and
, then the resulting velocity of the helicopter is:


The resultant velocity of the helicopter is
.