I can answer it in the comments, but can i ask what i’m supposed to do exactly? i remember learning about this stuff but i need the instructions.
Answer:
w = √[g /L (½ r²/L2 + 2/3 ) ]
When the mass of the cylinder changes if its external dimensions do not change the angular velocity DOES NOT CHANGE
Explanation:
We can simulate this system as a physical pendulum, which is a pendulum with a distributed mass, in this case the angular velocity is
w² = mg d / I
In this case, the distance d to the pivot point of half the length (L) of the cylinder, which we consider long and narrow
d = L / 2
The moment of inertia of a cylinder with respect to an axis at the end we can use the parallel axes theorem, it is approximately equal to that of a long bar plus the moment of inertia of the center of mass of the cylinder, this is tabulated
I = ¼ m r2 + ⅓ m L2
I = m (¼ r2 + ⅓ L2)
now let's use the concept of density to calculate the mass of the system
ρ = m / V
m = ρ V
the volume of a cylinder is
V = π r² L
m = ρ π r² L
let's substitute
w² = m g (L / 2) / m (¼ r² + ⅓ L²)
w² = g L / (½ r² + 2/3 L²)
L >> r
w = √[g /L (½ r²/L2 + 2/3 ) ]
When the mass of the cylinder changes if its external dimensions do not change the angular velocity DOES NOT CHANGE
Answer
22.5 m/s
Explanation
We shall use the trigonometric ratio cosine to find the horizontal component.
cos = adjacent/hypotenuse
Adjacent is the horizontal and hypotenuse is the fly speed.
cos 30° = horizontal / 26
horizontal velocity = 26 × cos 30°
= 26 × 0.866
= 22.5166
= 22.5 m/s
First of all, we need to convert the angular speed from rev/min into rev/s:
The angular acceleration is the variation of angular speed divided by the time:
And this is constant, so we can use the following equation to calculate the angle through which the engine has rotated:
so, 5 revolutions.
