Answer: angular acceleration = 
Given:
Distance from center of axis = 1.6 m
Time taken to complete one revolution = 4.7 sec
Therefore, we can evaluate the angular acceleration using the following formula:



= 
Answer:
magnitude: 21.6; direction: 33.7 degrees
Explanation:
When we multiply a vector by a scalar, we have to multiply each component of the vector by the scalar number. In this case, we have
vector: (-3,-2)
Scalar: -6
so the vector multiplied by the scalar will have components

The magnitude is given by Pythagorean's theorem:

and the direction is given by the arctan of the ratio between the y-component and the x-component:

<h2>
Answer: 277.777 m</h2>
Explanation:
The situation described here is parabolic movement. However, as we are told that the rock was<u> projected upward from the surface</u>, we will only use the equations related to the Y axis.
In this sense, the movement equations in the Y axis are:
(1)
(2)
Where:
is the rock's final position
is the rock's initial position
is the rock's initial velocity
is the final velocity
is the time the parabolic movement lasts
is the acceleration due to gravity at the surface of the moon
As we know
, equation (2) is rewritten as:
(3)
On the other hand, the maximum height is accomplished when
:
(4)
(5)
Finding
:
(6)
Substituting (6) in (3):
(7)
(8) Now we can calculate the maximum height of the rock
(9)
Finally:
Answer:
The angular momentum of a cylinder, when it is rotating with constant angular velocity is Lini =Iωi
. When two cylinders are added to the rotating cylinder, which are identical in their dimensions, the moment of inertia of the entire system increases (since mass increases). The final moment of inertia will be 3I
Since friction exist, all the cylinders start rotating with same angular velocity, the new angular velocity can be calculated using conservation of angular momentum
Thus, Iωi =3Iωf ⟹ωf =ωi/3 = 0.33ωi